KILLED
proof of input_dLjFj6PvB2.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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), 7 ms]
    (14) typed CpxTrs
    (15) RewriteLemmaProof [LOWER BOUND(ID), 334 ms]
    (16) BEST
        (17) proven lower bound
            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
            (19) BOUNDS(n^1, INF)
        (20) typed CpxTrs
            (21) RewriteLemmaProof [LOWER BOUND(ID), 46 ms]
            (22) typed CpxTrs
            (23) RewriteLemmaProof [LOWER BOUND(ID), 1155 ms]
            (24) typed CpxTrs
            (25) RewriteLemmaProof [LOWER BOUND(ID), 0 ms]
            (26) BOUNDS(1, INF)
(27) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(28) CpxWeightedTrs
    (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) CpxTypedWeightedTrs
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
        (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (36) CpxRNTS
        (37) InliningProof [UPPER BOUND(ID), 118 ms]
        (38) CpxRNTS
        (39) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CpxRNTS
        (41) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CpxRNTS
        (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (44) CpxRNTS
        (45) IntTrsBoundProof [UPPER BOUND(ID), 204 ms]
        (46) CpxRNTS
        (47) IntTrsBoundProof [UPPER BOUND(ID), 46 ms]
        (48) CpxRNTS
        (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (50) CpxRNTS
        (51) IntTrsBoundProof [UPPER BOUND(ID), 280 ms]
        (52) CpxRNTS
        (53) IntTrsBoundProof [UPPER BOUND(ID), 145 ms]
        (54) CpxRNTS
        (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (56) CpxRNTS
        (57) IntTrsBoundProof [UPPER BOUND(ID), 303 ms]
        (58) CpxRNTS
        (59) IntTrsBoundProof [UPPER BOUND(ID), 166 ms]
        (60) CpxRNTS
        (61) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (62) CpxRNTS
        (63) IntTrsBoundProof [UPPER BOUND(ID), 1330 ms]
        (64) CpxRNTS
        (65) IntTrsBoundProof [UPPER BOUND(ID), 146 ms]
        (66) CpxRNTS
        (67) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (68) CpxRNTS
        (69) IntTrsBoundProof [UPPER BOUND(ID), 1473 ms]
        (70) CpxRNTS
        (71) IntTrsBoundProof [UPPER BOUND(ID), 215 ms]
        (72) CpxRNTS
    (73) CompletionProof [UPPER BOUND(ID), 0 ms]
    (74) CpxTypedWeightedCompleteTrs
        (75) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (76) CpxRNTS
(77) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(78) CdtProblem
    (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CpxRelTRS
        (85) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (86) CpxTRS
        (87) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CpxWeightedTrs
            (89) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (90) CpxTypedWeightedTrs
            (91) CompletionProof [UPPER BOUND(ID), 0 ms]
            (92) CpxTypedWeightedCompleteTrs
                (93) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
                (94) CpxTypedWeightedCompleteTrs
                (95) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (96) CpxRNTS
                (97) InliningProof [UPPER BOUND(ID), 72 ms]
                (98) CpxRNTS
                (99) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
                (100) CpxRNTS
                (101) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
                (102) CpxRNTS
                (103) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (104) CpxRNTS
                (105) IntTrsBoundProof [UPPER BOUND(ID), 18 ms]
                (106) CpxRNTS
                (107) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
                (108) CpxRNTS
                (109) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (110) CpxRNTS
                (111) IntTrsBoundProof [UPPER BOUND(ID), 231 ms]
                (112) CpxRNTS
                (113) IntTrsBoundProof [UPPER BOUND(ID), 115 ms]
                (114) CpxRNTS
                (115) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (116) CpxRNTS
                (117) IntTrsBoundProof [UPPER BOUND(ID), 169 ms]
                (118) CpxRNTS
                (119) IntTrsBoundProof [UPPER BOUND(ID), 84 ms]
                (120) CpxRNTS
                (121) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (122) CpxRNTS
                (123) IntTrsBoundProof [UPPER BOUND(ID), 222 ms]
                (124) CpxRNTS
                (125) IntTrsBoundProof [UPPER BOUND(ID), 75 ms]
                (126) CpxRNTS
                (127) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (128) CpxRNTS
                (129) IntTrsBoundProof [UPPER BOUND(ID), 221 ms]
                (130) CpxRNTS
                (131) IntTrsBoundProof [UPPER BOUND(ID), 83 ms]
                (132) CpxRNTS
                (133) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (134) CpxRNTS
                (135) IntTrsBoundProof [UPPER BOUND(ID), 8542 ms]
                (136) CpxRNTS
                (137) IntTrsBoundProof [UPPER BOUND(ID), 350 ms]
                (138) CpxRNTS
                (139) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (140) CpxRNTS
                (141) IntTrsBoundProof [UPPER BOUND(ID), 838 ms]
                (142) CpxRNTS
                (143) IntTrsBoundProof [UPPER BOUND(ID), 320 ms]
                (144) CpxRNTS
                (145) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (146) CpxRNTS
                (147) IntTrsBoundProof [UPPER BOUND(ID), 1297 ms]
                (148) CpxRNTS
                (149) IntTrsBoundProof [UPPER BOUND(ID), 769 ms]
                (150) CpxRNTS
            (151) CompletionProof [UPPER BOUND(ID), 0 ms]
            (152) CpxTypedWeightedCompleteTrs
                (153) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (154) CpxRNTS
    (155) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 104 ms]
    (156) CdtProblem
        (157) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 28 ms]
        (158) CdtProblem
        (159) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 72 ms]
        (160) CdtProblem
        (161) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
        (162) CdtProblem
        (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (164) CdtProblem
        (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (166) CdtProblem
        (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (168) CdtProblem
        (169) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (170) CdtProblem
        (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (174) CdtProblem
        (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (176) CdtProblem
        (177) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (178) CdtProblem
        (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (180) CdtProblem
        (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (182) CdtProblem
        (183) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
        (184) CdtProblem
        (185) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms]
        (186) CdtProblem
        (187) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (188) CdtProblem
        (189) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (190) CdtProblem
        (191) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 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), 0 ms]
        (198) CdtProblem
        (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (200) CdtProblem
        (201) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (202) CdtProblem
        (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 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), 0 ms]
        (218) CdtProblem
        (219) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (220) CdtProblem
        (221) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (222) CdtProblem
        (223) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (224) CdtProblem
        (225) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (226) CdtProblem
        (227) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (228) CdtProblem
        (229) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (230) CdtProblem
        (231) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (232) CdtProblem
        (233) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (234) CdtProblem
        (235) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (236) CdtProblem
        (237) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (238) CdtProblem
        (239) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (240) CdtProblem
        (241) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 42 ms]
        (242) CdtProblem
        (243) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 21 ms]
        (244) CdtProblem
        (245) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (246) CdtProblem
        (247) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms]
        (248) CdtProblem
        (249) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (250) CdtProblem
        (251) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (252) CdtProblem


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

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   from(X) -> cons(X, n__from(s(X)))
   sel(0, cons(X, XS)) -> X
   sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
   minus(X, 0) -> 0
   minus(s(X), s(Y)) -> minus(X, Y)
   quot(0, s(Y)) -> 0
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
   zWquot(XS, nil) -> nil
   zWquot(nil, XS) -> nil
   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
   from(X) -> n__from(X)
   zWquot(X1, X2) -> n__zWquot(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__zWquot(X1, X2)) -> zWquot(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(s(X)))
   sel(0', cons(X, XS)) -> X
   sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
   minus(X, 0') -> 0'
   minus(s(X), s(Y)) -> minus(X, Y)
   quot(0', s(Y)) -> 0'
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
   zWquot(XS, nil) -> nil
   zWquot(nil, XS) -> nil
   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
   from(X) -> n__from(X)
   zWquot(X1, X2) -> n__zWquot(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__zWquot(X1, X2)) -> zWquot(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(s(X)))
   sel(0, cons(X, XS)) -> X
   sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
   minus(X, 0) -> 0
   minus(s(X), s(Y)) -> minus(X, Y)
   quot(0, s(Y)) -> 0
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
   zWquot(XS, nil) -> nil
   zWquot(nil, XS) -> nil
   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
   from(X) -> n__from(X)
   zWquot(X1, X2) -> n__zWquot(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__zWquot(X1, X2)) -> zWquot(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(s(z0)))
   from(z0) -> n__from(z0)
   sel(0, cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
Tuples:
   FROM(z0) -> c
   FROM(z0) -> c1
   SEL(0, cons(z0, z1)) -> c2
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(z0, 0) -> c4
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(0, s(z0)) -> c6
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(z0, nil) -> c8
   ZWQUOT(nil, z0) -> c9
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ZWQUOT(z0, z1) -> c13
   ACTIVATE(n__from(z0)) -> c14(FROM(z0))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ACTIVATE(z0) -> c16
S tuples:
   FROM(z0) -> c
   FROM(z0) -> c1
   SEL(0, cons(z0, z1)) -> c2
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(z0, 0) -> c4
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(0, s(z0)) -> c6
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(z0, nil) -> c8
   ZWQUOT(nil, z0) -> c9
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ZWQUOT(z0, z1) -> c13
   ACTIVATE(n__from(z0)) -> c14(FROM(z0))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ACTIVATE(z0) -> c16
K tuples:none
Defined Rule Symbols:   from_1, sel_2, minus_2, quot_2, zWquot_2, activate_1

Defined Pair Symbols:   FROM_1, SEL_2, MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c, c1, c2, c3_2, c4, c5_1, c6, c7_2, c8, c9, c10_1, c11_1, c12_1, c13, c14_1, c15_1, c16


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

(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
   FROM(z0) -> c1
   SEL(0, cons(z0, z1)) -> c2
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(z0, 0) -> c4
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(0, s(z0)) -> c6
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(z0, nil) -> c8
   ZWQUOT(nil, z0) -> c9
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ZWQUOT(z0, z1) -> c13
   ACTIVATE(n__from(z0)) -> c14(FROM(z0))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ACTIVATE(z0) -> c16

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

   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   sel(0, cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(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
   FROM(z0) -> c1
   SEL(0', cons(z0, z1)) -> c2
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(z0, 0') -> c4
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(0', s(z0)) -> c6
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(z0, nil) -> c8
   ZWQUOT(nil, z0) -> c9
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ZWQUOT(z0, z1) -> c13
   ACTIVATE(n__from(z0)) -> c14(FROM(z0))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ACTIVATE(z0) -> c16

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

   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   sel(0', cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
   minus(z0, 0') -> 0'
   minus(s(z0), s(z1)) -> minus(z0, z1)
   quot(0', s(z0)) -> 0'
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0

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

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

(12)
Obligation:
Innermost TRS:
Rules:
FROM(z0) -> c
FROM(z0) -> c1
SEL(0', cons(z0, z1)) -> c2
SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
MINUS(z0, 0') -> c4
MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
QUOT(0', s(z0)) -> c6
QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
ZWQUOT(z0, nil) -> c8
ZWQUOT(nil, z0) -> c9
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
ZWQUOT(z0, z1) -> c13
ACTIVATE(n__from(z0)) -> c14(FROM(z0))
ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
ACTIVATE(z0) -> c16
from(z0) -> cons(z0, n__from(s(z0)))
from(z0) -> n__from(z0)
sel(0', cons(z0, z1)) -> z0
sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
minus(z0, 0') -> 0'
minus(s(z0), s(z1)) -> minus(z0, z1)
quot(0', s(z0)) -> 0'
quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
zWquot(z0, nil) -> nil
zWquot(nil, z0) -> nil
zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
zWquot(z0, z1) -> n__zWquot(z0, z1)
activate(n__from(z0)) -> from(z0)
activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
activate(z0) -> z0

Types:
FROM :: 0':s -> c:c1
c :: c:c1
c1 :: c:c1
SEL :: 0':s -> cons:nil:n__from:n__zWquot -> c2:c3
0' :: 0':s
cons :: 0':s -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c2 :: c2:c3
s :: 0':s -> 0':s
c3 :: c2:c3 -> c14:c15:c16 -> c2:c3
activate :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
ACTIVATE :: cons:nil:n__from:n__zWquot -> c14:c15:c16
MINUS :: 0':s -> 0':s -> c4:c5
c4 :: c4:c5
c5 :: c4:c5 -> c4:c5
QUOT :: 0':s -> 0':s -> c6:c7
c6 :: c6:c7
c7 :: c6:c7 -> c4:c5 -> c6:c7
minus :: 0':s -> 0':s -> 0':s
ZWQUOT :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> c8:c9:c10:c11:c12:c13
nil :: cons:nil:n__from:n__zWquot
c8 :: c8:c9:c10:c11:c12:c13
c9 :: c8:c9:c10:c11:c12:c13
c10 :: c6:c7 -> c8:c9:c10:c11:c12:c13
c11 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c12 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c13 :: c8:c9:c10:c11:c12:c13
n__from :: 0':s -> cons:nil:n__from:n__zWquot
c14 :: c:c1 -> c14:c15:c16
n__zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c15 :: c8:c9:c10:c11:c12:c13 -> c14:c15:c16
c16 :: c14:c15:c16
from :: 0':s -> cons:nil:n__from:n__zWquot
sel :: 0':s -> cons:nil:n__from:n__zWquot -> 0':s
quot :: 0':s -> 0':s -> 0':s
zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
hole_c:c11_17 :: c:c1
hole_0':s2_17 :: 0':s
hole_c2:c33_17 :: c2:c3
hole_cons:nil:n__from:n__zWquot4_17 :: cons:nil:n__from:n__zWquot
hole_c14:c15:c165_17 :: c14:c15:c16
hole_c4:c56_17 :: c4:c5
hole_c6:c77_17 :: c6:c7
hole_c8:c9:c10:c11:c12:c138_17 :: c8:c9:c10:c11:c12:c13
gen_0':s9_17 :: Nat -> 0':s
gen_c2:c310_17 :: Nat -> c2:c3
gen_cons:nil:n__from:n__zWquot11_17 :: Nat -> cons:nil:n__from:n__zWquot
gen_c4:c512_17 :: Nat -> c4:c5
gen_c6:c713_17 :: Nat -> c6:c7

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

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
SEL, activate, ACTIVATE, MINUS, QUOT, minus, sel, quot

They will be analysed ascendingly in the following order:
activate < SEL
ACTIVATE < SEL
activate < sel
quot < activate
QUOT < ACTIVATE
MINUS < QUOT
minus < QUOT
minus < quot

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

(14)
Obligation:
Innermost TRS:
Rules:
FROM(z0) -> c
FROM(z0) -> c1
SEL(0', cons(z0, z1)) -> c2
SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
MINUS(z0, 0') -> c4
MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
QUOT(0', s(z0)) -> c6
QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
ZWQUOT(z0, nil) -> c8
ZWQUOT(nil, z0) -> c9
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
ZWQUOT(z0, z1) -> c13
ACTIVATE(n__from(z0)) -> c14(FROM(z0))
ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
ACTIVATE(z0) -> c16
from(z0) -> cons(z0, n__from(s(z0)))
from(z0) -> n__from(z0)
sel(0', cons(z0, z1)) -> z0
sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
minus(z0, 0') -> 0'
minus(s(z0), s(z1)) -> minus(z0, z1)
quot(0', s(z0)) -> 0'
quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
zWquot(z0, nil) -> nil
zWquot(nil, z0) -> nil
zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
zWquot(z0, z1) -> n__zWquot(z0, z1)
activate(n__from(z0)) -> from(z0)
activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
activate(z0) -> z0

Types:
FROM :: 0':s -> c:c1
c :: c:c1
c1 :: c:c1
SEL :: 0':s -> cons:nil:n__from:n__zWquot -> c2:c3
0' :: 0':s
cons :: 0':s -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c2 :: c2:c3
s :: 0':s -> 0':s
c3 :: c2:c3 -> c14:c15:c16 -> c2:c3
activate :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
ACTIVATE :: cons:nil:n__from:n__zWquot -> c14:c15:c16
MINUS :: 0':s -> 0':s -> c4:c5
c4 :: c4:c5
c5 :: c4:c5 -> c4:c5
QUOT :: 0':s -> 0':s -> c6:c7
c6 :: c6:c7
c7 :: c6:c7 -> c4:c5 -> c6:c7
minus :: 0':s -> 0':s -> 0':s
ZWQUOT :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> c8:c9:c10:c11:c12:c13
nil :: cons:nil:n__from:n__zWquot
c8 :: c8:c9:c10:c11:c12:c13
c9 :: c8:c9:c10:c11:c12:c13
c10 :: c6:c7 -> c8:c9:c10:c11:c12:c13
c11 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c12 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c13 :: c8:c9:c10:c11:c12:c13
n__from :: 0':s -> cons:nil:n__from:n__zWquot
c14 :: c:c1 -> c14:c15:c16
n__zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c15 :: c8:c9:c10:c11:c12:c13 -> c14:c15:c16
c16 :: c14:c15:c16
from :: 0':s -> cons:nil:n__from:n__zWquot
sel :: 0':s -> cons:nil:n__from:n__zWquot -> 0':s
quot :: 0':s -> 0':s -> 0':s
zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
hole_c:c11_17 :: c:c1
hole_0':s2_17 :: 0':s
hole_c2:c33_17 :: c2:c3
hole_cons:nil:n__from:n__zWquot4_17 :: cons:nil:n__from:n__zWquot
hole_c14:c15:c165_17 :: c14:c15:c16
hole_c4:c56_17 :: c4:c5
hole_c6:c77_17 :: c6:c7
hole_c8:c9:c10:c11:c12:c138_17 :: c8:c9:c10:c11:c12:c13
gen_0':s9_17 :: Nat -> 0':s
gen_c2:c310_17 :: Nat -> c2:c3
gen_cons:nil:n__from:n__zWquot11_17 :: Nat -> cons:nil:n__from:n__zWquot
gen_c4:c512_17 :: Nat -> c4:c5
gen_c6:c713_17 :: Nat -> c6:c7


Generator Equations:
gen_0':s9_17(0) <=> 0'
gen_0':s9_17(+(x, 1)) <=> s(gen_0':s9_17(x))
gen_c2:c310_17(0) <=> c2
gen_c2:c310_17(+(x, 1)) <=> c3(gen_c2:c310_17(x), c14(c))
gen_cons:nil:n__from:n__zWquot11_17(0) <=> nil
gen_cons:nil:n__from:n__zWquot11_17(+(x, 1)) <=> cons(0', gen_cons:nil:n__from:n__zWquot11_17(x))
gen_c4:c512_17(0) <=> c4
gen_c4:c512_17(+(x, 1)) <=> c5(gen_c4:c512_17(x))
gen_c6:c713_17(0) <=> c6
gen_c6:c713_17(+(x, 1)) <=> c7(gen_c6:c713_17(x), c4)


The following defined symbols remain to be analysed:
MINUS, SEL, activate, ACTIVATE, QUOT, minus, sel, quot

They will be analysed ascendingly in the following order:
activate < SEL
ACTIVATE < SEL
activate < sel
quot < activate
QUOT < ACTIVATE
MINUS < QUOT
minus < QUOT
minus < quot

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

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MINUS(gen_0':s9_17(n15_17), gen_0':s9_17(n15_17)) -> gen_c4:c512_17(n15_17), rt in Omega(1 + n15_17)

Induction Base:
MINUS(gen_0':s9_17(0), gen_0':s9_17(0)) ->_R^Omega(1)
c4

Induction Step:
MINUS(gen_0':s9_17(+(n15_17, 1)), gen_0':s9_17(+(n15_17, 1))) ->_R^Omega(1)
c5(MINUS(gen_0':s9_17(n15_17), gen_0':s9_17(n15_17))) ->_IH
c5(gen_c4:c512_17(c16_17))

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

(16)
Complex Obligation (BEST)

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

(17)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
FROM(z0) -> c
FROM(z0) -> c1
SEL(0', cons(z0, z1)) -> c2
SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
MINUS(z0, 0') -> c4
MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
QUOT(0', s(z0)) -> c6
QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
ZWQUOT(z0, nil) -> c8
ZWQUOT(nil, z0) -> c9
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
ZWQUOT(z0, z1) -> c13
ACTIVATE(n__from(z0)) -> c14(FROM(z0))
ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
ACTIVATE(z0) -> c16
from(z0) -> cons(z0, n__from(s(z0)))
from(z0) -> n__from(z0)
sel(0', cons(z0, z1)) -> z0
sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
minus(z0, 0') -> 0'
minus(s(z0), s(z1)) -> minus(z0, z1)
quot(0', s(z0)) -> 0'
quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
zWquot(z0, nil) -> nil
zWquot(nil, z0) -> nil
zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
zWquot(z0, z1) -> n__zWquot(z0, z1)
activate(n__from(z0)) -> from(z0)
activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
activate(z0) -> z0

Types:
FROM :: 0':s -> c:c1
c :: c:c1
c1 :: c:c1
SEL :: 0':s -> cons:nil:n__from:n__zWquot -> c2:c3
0' :: 0':s
cons :: 0':s -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c2 :: c2:c3
s :: 0':s -> 0':s
c3 :: c2:c3 -> c14:c15:c16 -> c2:c3
activate :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
ACTIVATE :: cons:nil:n__from:n__zWquot -> c14:c15:c16
MINUS :: 0':s -> 0':s -> c4:c5
c4 :: c4:c5
c5 :: c4:c5 -> c4:c5
QUOT :: 0':s -> 0':s -> c6:c7
c6 :: c6:c7
c7 :: c6:c7 -> c4:c5 -> c6:c7
minus :: 0':s -> 0':s -> 0':s
ZWQUOT :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> c8:c9:c10:c11:c12:c13
nil :: cons:nil:n__from:n__zWquot
c8 :: c8:c9:c10:c11:c12:c13
c9 :: c8:c9:c10:c11:c12:c13
c10 :: c6:c7 -> c8:c9:c10:c11:c12:c13
c11 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c12 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c13 :: c8:c9:c10:c11:c12:c13
n__from :: 0':s -> cons:nil:n__from:n__zWquot
c14 :: c:c1 -> c14:c15:c16
n__zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c15 :: c8:c9:c10:c11:c12:c13 -> c14:c15:c16
c16 :: c14:c15:c16
from :: 0':s -> cons:nil:n__from:n__zWquot
sel :: 0':s -> cons:nil:n__from:n__zWquot -> 0':s
quot :: 0':s -> 0':s -> 0':s
zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
hole_c:c11_17 :: c:c1
hole_0':s2_17 :: 0':s
hole_c2:c33_17 :: c2:c3
hole_cons:nil:n__from:n__zWquot4_17 :: cons:nil:n__from:n__zWquot
hole_c14:c15:c165_17 :: c14:c15:c16
hole_c4:c56_17 :: c4:c5
hole_c6:c77_17 :: c6:c7
hole_c8:c9:c10:c11:c12:c138_17 :: c8:c9:c10:c11:c12:c13
gen_0':s9_17 :: Nat -> 0':s
gen_c2:c310_17 :: Nat -> c2:c3
gen_cons:nil:n__from:n__zWquot11_17 :: Nat -> cons:nil:n__from:n__zWquot
gen_c4:c512_17 :: Nat -> c4:c5
gen_c6:c713_17 :: Nat -> c6:c7


Generator Equations:
gen_0':s9_17(0) <=> 0'
gen_0':s9_17(+(x, 1)) <=> s(gen_0':s9_17(x))
gen_c2:c310_17(0) <=> c2
gen_c2:c310_17(+(x, 1)) <=> c3(gen_c2:c310_17(x), c14(c))
gen_cons:nil:n__from:n__zWquot11_17(0) <=> nil
gen_cons:nil:n__from:n__zWquot11_17(+(x, 1)) <=> cons(0', gen_cons:nil:n__from:n__zWquot11_17(x))
gen_c4:c512_17(0) <=> c4
gen_c4:c512_17(+(x, 1)) <=> c5(gen_c4:c512_17(x))
gen_c6:c713_17(0) <=> c6
gen_c6:c713_17(+(x, 1)) <=> c7(gen_c6:c713_17(x), c4)


The following defined symbols remain to be analysed:
MINUS, SEL, activate, ACTIVATE, QUOT, minus, sel, quot

They will be analysed ascendingly in the following order:
activate < SEL
ACTIVATE < SEL
activate < sel
quot < activate
QUOT < ACTIVATE
MINUS < QUOT
minus < QUOT
minus < quot

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

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

(19)
BOUNDS(n^1, INF)

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

(20)
Obligation:
Innermost TRS:
Rules:
FROM(z0) -> c
FROM(z0) -> c1
SEL(0', cons(z0, z1)) -> c2
SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
MINUS(z0, 0') -> c4
MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
QUOT(0', s(z0)) -> c6
QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
ZWQUOT(z0, nil) -> c8
ZWQUOT(nil, z0) -> c9
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
ZWQUOT(z0, z1) -> c13
ACTIVATE(n__from(z0)) -> c14(FROM(z0))
ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
ACTIVATE(z0) -> c16
from(z0) -> cons(z0, n__from(s(z0)))
from(z0) -> n__from(z0)
sel(0', cons(z0, z1)) -> z0
sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
minus(z0, 0') -> 0'
minus(s(z0), s(z1)) -> minus(z0, z1)
quot(0', s(z0)) -> 0'
quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
zWquot(z0, nil) -> nil
zWquot(nil, z0) -> nil
zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
zWquot(z0, z1) -> n__zWquot(z0, z1)
activate(n__from(z0)) -> from(z0)
activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
activate(z0) -> z0

Types:
FROM :: 0':s -> c:c1
c :: c:c1
c1 :: c:c1
SEL :: 0':s -> cons:nil:n__from:n__zWquot -> c2:c3
0' :: 0':s
cons :: 0':s -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c2 :: c2:c3
s :: 0':s -> 0':s
c3 :: c2:c3 -> c14:c15:c16 -> c2:c3
activate :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
ACTIVATE :: cons:nil:n__from:n__zWquot -> c14:c15:c16
MINUS :: 0':s -> 0':s -> c4:c5
c4 :: c4:c5
c5 :: c4:c5 -> c4:c5
QUOT :: 0':s -> 0':s -> c6:c7
c6 :: c6:c7
c7 :: c6:c7 -> c4:c5 -> c6:c7
minus :: 0':s -> 0':s -> 0':s
ZWQUOT :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> c8:c9:c10:c11:c12:c13
nil :: cons:nil:n__from:n__zWquot
c8 :: c8:c9:c10:c11:c12:c13
c9 :: c8:c9:c10:c11:c12:c13
c10 :: c6:c7 -> c8:c9:c10:c11:c12:c13
c11 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c12 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c13 :: c8:c9:c10:c11:c12:c13
n__from :: 0':s -> cons:nil:n__from:n__zWquot
c14 :: c:c1 -> c14:c15:c16
n__zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c15 :: c8:c9:c10:c11:c12:c13 -> c14:c15:c16
c16 :: c14:c15:c16
from :: 0':s -> cons:nil:n__from:n__zWquot
sel :: 0':s -> cons:nil:n__from:n__zWquot -> 0':s
quot :: 0':s -> 0':s -> 0':s
zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
hole_c:c11_17 :: c:c1
hole_0':s2_17 :: 0':s
hole_c2:c33_17 :: c2:c3
hole_cons:nil:n__from:n__zWquot4_17 :: cons:nil:n__from:n__zWquot
hole_c14:c15:c165_17 :: c14:c15:c16
hole_c4:c56_17 :: c4:c5
hole_c6:c77_17 :: c6:c7
hole_c8:c9:c10:c11:c12:c138_17 :: c8:c9:c10:c11:c12:c13
gen_0':s9_17 :: Nat -> 0':s
gen_c2:c310_17 :: Nat -> c2:c3
gen_cons:nil:n__from:n__zWquot11_17 :: Nat -> cons:nil:n__from:n__zWquot
gen_c4:c512_17 :: Nat -> c4:c5
gen_c6:c713_17 :: Nat -> c6:c7


Lemmas:
MINUS(gen_0':s9_17(n15_17), gen_0':s9_17(n15_17)) -> gen_c4:c512_17(n15_17), rt in Omega(1 + n15_17)


Generator Equations:
gen_0':s9_17(0) <=> 0'
gen_0':s9_17(+(x, 1)) <=> s(gen_0':s9_17(x))
gen_c2:c310_17(0) <=> c2
gen_c2:c310_17(+(x, 1)) <=> c3(gen_c2:c310_17(x), c14(c))
gen_cons:nil:n__from:n__zWquot11_17(0) <=> nil
gen_cons:nil:n__from:n__zWquot11_17(+(x, 1)) <=> cons(0', gen_cons:nil:n__from:n__zWquot11_17(x))
gen_c4:c512_17(0) <=> c4
gen_c4:c512_17(+(x, 1)) <=> c5(gen_c4:c512_17(x))
gen_c6:c713_17(0) <=> c6
gen_c6:c713_17(+(x, 1)) <=> c7(gen_c6:c713_17(x), c4)


The following defined symbols remain to be analysed:
minus, SEL, activate, ACTIVATE, QUOT, sel, quot

They will be analysed ascendingly in the following order:
activate < SEL
ACTIVATE < SEL
activate < sel
quot < activate
QUOT < ACTIVATE
minus < QUOT
minus < quot

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

(21) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
minus(gen_0':s9_17(n608_17), gen_0':s9_17(n608_17)) -> gen_0':s9_17(0), rt in Omega(0)

Induction Base:
minus(gen_0':s9_17(0), gen_0':s9_17(0)) ->_R^Omega(0)
0'

Induction Step:
minus(gen_0':s9_17(+(n608_17, 1)), gen_0':s9_17(+(n608_17, 1))) ->_R^Omega(0)
minus(gen_0':s9_17(n608_17), gen_0':s9_17(n608_17)) ->_IH
gen_0':s9_17(0)

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

(22)
Obligation:
Innermost TRS:
Rules:
FROM(z0) -> c
FROM(z0) -> c1
SEL(0', cons(z0, z1)) -> c2
SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
MINUS(z0, 0') -> c4
MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
QUOT(0', s(z0)) -> c6
QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
ZWQUOT(z0, nil) -> c8
ZWQUOT(nil, z0) -> c9
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
ZWQUOT(z0, z1) -> c13
ACTIVATE(n__from(z0)) -> c14(FROM(z0))
ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
ACTIVATE(z0) -> c16
from(z0) -> cons(z0, n__from(s(z0)))
from(z0) -> n__from(z0)
sel(0', cons(z0, z1)) -> z0
sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
minus(z0, 0') -> 0'
minus(s(z0), s(z1)) -> minus(z0, z1)
quot(0', s(z0)) -> 0'
quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
zWquot(z0, nil) -> nil
zWquot(nil, z0) -> nil
zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
zWquot(z0, z1) -> n__zWquot(z0, z1)
activate(n__from(z0)) -> from(z0)
activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
activate(z0) -> z0

Types:
FROM :: 0':s -> c:c1
c :: c:c1
c1 :: c:c1
SEL :: 0':s -> cons:nil:n__from:n__zWquot -> c2:c3
0' :: 0':s
cons :: 0':s -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c2 :: c2:c3
s :: 0':s -> 0':s
c3 :: c2:c3 -> c14:c15:c16 -> c2:c3
activate :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
ACTIVATE :: cons:nil:n__from:n__zWquot -> c14:c15:c16
MINUS :: 0':s -> 0':s -> c4:c5
c4 :: c4:c5
c5 :: c4:c5 -> c4:c5
QUOT :: 0':s -> 0':s -> c6:c7
c6 :: c6:c7
c7 :: c6:c7 -> c4:c5 -> c6:c7
minus :: 0':s -> 0':s -> 0':s
ZWQUOT :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> c8:c9:c10:c11:c12:c13
nil :: cons:nil:n__from:n__zWquot
c8 :: c8:c9:c10:c11:c12:c13
c9 :: c8:c9:c10:c11:c12:c13
c10 :: c6:c7 -> c8:c9:c10:c11:c12:c13
c11 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c12 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c13 :: c8:c9:c10:c11:c12:c13
n__from :: 0':s -> cons:nil:n__from:n__zWquot
c14 :: c:c1 -> c14:c15:c16
n__zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c15 :: c8:c9:c10:c11:c12:c13 -> c14:c15:c16
c16 :: c14:c15:c16
from :: 0':s -> cons:nil:n__from:n__zWquot
sel :: 0':s -> cons:nil:n__from:n__zWquot -> 0':s
quot :: 0':s -> 0':s -> 0':s
zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
hole_c:c11_17 :: c:c1
hole_0':s2_17 :: 0':s
hole_c2:c33_17 :: c2:c3
hole_cons:nil:n__from:n__zWquot4_17 :: cons:nil:n__from:n__zWquot
hole_c14:c15:c165_17 :: c14:c15:c16
hole_c4:c56_17 :: c4:c5
hole_c6:c77_17 :: c6:c7
hole_c8:c9:c10:c11:c12:c138_17 :: c8:c9:c10:c11:c12:c13
gen_0':s9_17 :: Nat -> 0':s
gen_c2:c310_17 :: Nat -> c2:c3
gen_cons:nil:n__from:n__zWquot11_17 :: Nat -> cons:nil:n__from:n__zWquot
gen_c4:c512_17 :: Nat -> c4:c5
gen_c6:c713_17 :: Nat -> c6:c7


Lemmas:
MINUS(gen_0':s9_17(n15_17), gen_0':s9_17(n15_17)) -> gen_c4:c512_17(n15_17), rt in Omega(1 + n15_17)
minus(gen_0':s9_17(n608_17), gen_0':s9_17(n608_17)) -> gen_0':s9_17(0), rt in Omega(0)


Generator Equations:
gen_0':s9_17(0) <=> 0'
gen_0':s9_17(+(x, 1)) <=> s(gen_0':s9_17(x))
gen_c2:c310_17(0) <=> c2
gen_c2:c310_17(+(x, 1)) <=> c3(gen_c2:c310_17(x), c14(c))
gen_cons:nil:n__from:n__zWquot11_17(0) <=> nil
gen_cons:nil:n__from:n__zWquot11_17(+(x, 1)) <=> cons(0', gen_cons:nil:n__from:n__zWquot11_17(x))
gen_c4:c512_17(0) <=> c4
gen_c4:c512_17(+(x, 1)) <=> c5(gen_c4:c512_17(x))
gen_c6:c713_17(0) <=> c6
gen_c6:c713_17(+(x, 1)) <=> c7(gen_c6:c713_17(x), c4)


The following defined symbols remain to be analysed:
QUOT, SEL, activate, ACTIVATE, sel, quot

They will be analysed ascendingly in the following order:
activate < SEL
ACTIVATE < SEL
activate < sel
quot < activate
QUOT < ACTIVATE

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

(23) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
SEL(gen_0':s9_17(n2153_17), gen_cons:nil:n__from:n__zWquot11_17(+(1, n2153_17))) -> *14_17, rt in Omega(n2153_17)

Induction Base:
SEL(gen_0':s9_17(0), gen_cons:nil:n__from:n__zWquot11_17(+(1, 0)))

Induction Step:
SEL(gen_0':s9_17(+(n2153_17, 1)), gen_cons:nil:n__from:n__zWquot11_17(+(1, +(n2153_17, 1)))) ->_R^Omega(1)
c3(SEL(gen_0':s9_17(n2153_17), activate(gen_cons:nil:n__from:n__zWquot11_17(+(1, n2153_17)))), ACTIVATE(gen_cons:nil:n__from:n__zWquot11_17(+(1, n2153_17)))) ->_R^Omega(0)
c3(SEL(gen_0':s9_17(n2153_17), gen_cons:nil:n__from:n__zWquot11_17(+(1, n2153_17))), ACTIVATE(gen_cons:nil:n__from:n__zWquot11_17(+(1, n2153_17)))) ->_IH
c3(*14_17, ACTIVATE(gen_cons:nil:n__from:n__zWquot11_17(+(1, n2153_17)))) ->_R^Omega(1)
c3(*14_17, c16)

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

(24)
Obligation:
Innermost TRS:
Rules:
FROM(z0) -> c
FROM(z0) -> c1
SEL(0', cons(z0, z1)) -> c2
SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
MINUS(z0, 0') -> c4
MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
QUOT(0', s(z0)) -> c6
QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
ZWQUOT(z0, nil) -> c8
ZWQUOT(nil, z0) -> c9
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
ZWQUOT(z0, z1) -> c13
ACTIVATE(n__from(z0)) -> c14(FROM(z0))
ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
ACTIVATE(z0) -> c16
from(z0) -> cons(z0, n__from(s(z0)))
from(z0) -> n__from(z0)
sel(0', cons(z0, z1)) -> z0
sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
minus(z0, 0') -> 0'
minus(s(z0), s(z1)) -> minus(z0, z1)
quot(0', s(z0)) -> 0'
quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
zWquot(z0, nil) -> nil
zWquot(nil, z0) -> nil
zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
zWquot(z0, z1) -> n__zWquot(z0, z1)
activate(n__from(z0)) -> from(z0)
activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
activate(z0) -> z0

Types:
FROM :: 0':s -> c:c1
c :: c:c1
c1 :: c:c1
SEL :: 0':s -> cons:nil:n__from:n__zWquot -> c2:c3
0' :: 0':s
cons :: 0':s -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c2 :: c2:c3
s :: 0':s -> 0':s
c3 :: c2:c3 -> c14:c15:c16 -> c2:c3
activate :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
ACTIVATE :: cons:nil:n__from:n__zWquot -> c14:c15:c16
MINUS :: 0':s -> 0':s -> c4:c5
c4 :: c4:c5
c5 :: c4:c5 -> c4:c5
QUOT :: 0':s -> 0':s -> c6:c7
c6 :: c6:c7
c7 :: c6:c7 -> c4:c5 -> c6:c7
minus :: 0':s -> 0':s -> 0':s
ZWQUOT :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> c8:c9:c10:c11:c12:c13
nil :: cons:nil:n__from:n__zWquot
c8 :: c8:c9:c10:c11:c12:c13
c9 :: c8:c9:c10:c11:c12:c13
c10 :: c6:c7 -> c8:c9:c10:c11:c12:c13
c11 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c12 :: c14:c15:c16 -> c8:c9:c10:c11:c12:c13
c13 :: c8:c9:c10:c11:c12:c13
n__from :: 0':s -> cons:nil:n__from:n__zWquot
c14 :: c:c1 -> c14:c15:c16
n__zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
c15 :: c8:c9:c10:c11:c12:c13 -> c14:c15:c16
c16 :: c14:c15:c16
from :: 0':s -> cons:nil:n__from:n__zWquot
sel :: 0':s -> cons:nil:n__from:n__zWquot -> 0':s
quot :: 0':s -> 0':s -> 0':s
zWquot :: cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot -> cons:nil:n__from:n__zWquot
hole_c:c11_17 :: c:c1
hole_0':s2_17 :: 0':s
hole_c2:c33_17 :: c2:c3
hole_cons:nil:n__from:n__zWquot4_17 :: cons:nil:n__from:n__zWquot
hole_c14:c15:c165_17 :: c14:c15:c16
hole_c4:c56_17 :: c4:c5
hole_c6:c77_17 :: c6:c7
hole_c8:c9:c10:c11:c12:c138_17 :: c8:c9:c10:c11:c12:c13
gen_0':s9_17 :: Nat -> 0':s
gen_c2:c310_17 :: Nat -> c2:c3
gen_cons:nil:n__from:n__zWquot11_17 :: Nat -> cons:nil:n__from:n__zWquot
gen_c4:c512_17 :: Nat -> c4:c5
gen_c6:c713_17 :: Nat -> c6:c7


Lemmas:
MINUS(gen_0':s9_17(n15_17), gen_0':s9_17(n15_17)) -> gen_c4:c512_17(n15_17), rt in Omega(1 + n15_17)
minus(gen_0':s9_17(n608_17), gen_0':s9_17(n608_17)) -> gen_0':s9_17(0), rt in Omega(0)
SEL(gen_0':s9_17(n2153_17), gen_cons:nil:n__from:n__zWquot11_17(+(1, n2153_17))) -> *14_17, rt in Omega(n2153_17)


Generator Equations:
gen_0':s9_17(0) <=> 0'
gen_0':s9_17(+(x, 1)) <=> s(gen_0':s9_17(x))
gen_c2:c310_17(0) <=> c2
gen_c2:c310_17(+(x, 1)) <=> c3(gen_c2:c310_17(x), c14(c))
gen_cons:nil:n__from:n__zWquot11_17(0) <=> nil
gen_cons:nil:n__from:n__zWquot11_17(+(x, 1)) <=> cons(0', gen_cons:nil:n__from:n__zWquot11_17(x))
gen_c4:c512_17(0) <=> c4
gen_c4:c512_17(+(x, 1)) <=> c5(gen_c4:c512_17(x))
gen_c6:c713_17(0) <=> c6
gen_c6:c713_17(+(x, 1)) <=> c7(gen_c6:c713_17(x), c4)


The following defined symbols remain to be analysed:
sel
----------------------------------------

(25) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
sel(gen_0':s9_17(n6547_17), gen_cons:nil:n__from:n__zWquot11_17(+(1, n6547_17))) -> gen_0':s9_17(0), rt in Omega(0)

Induction Base:
sel(gen_0':s9_17(0), gen_cons:nil:n__from:n__zWquot11_17(+(1, 0))) ->_R^Omega(0)
0'

Induction Step:
sel(gen_0':s9_17(+(n6547_17, 1)), gen_cons:nil:n__from:n__zWquot11_17(+(1, +(n6547_17, 1)))) ->_R^Omega(0)
sel(gen_0':s9_17(n6547_17), activate(gen_cons:nil:n__from:n__zWquot11_17(+(1, n6547_17)))) ->_R^Omega(0)
sel(gen_0':s9_17(n6547_17), gen_cons:nil:n__from:n__zWquot11_17(+(1, n6547_17))) ->_IH
gen_0':s9_17(0)

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

(26)
BOUNDS(1, INF)

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

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

(28)
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(s(X))) [1]
   sel(0, cons(X, XS)) -> X [1]
   sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) [1]
   minus(X, 0) -> 0 [1]
   minus(s(X), s(Y)) -> minus(X, Y) [1]
   quot(0, s(Y)) -> 0 [1]
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) [1]
   zWquot(XS, nil) -> nil [1]
   zWquot(nil, XS) -> nil [1]
   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) [1]
   from(X) -> n__from(X) [1]
   zWquot(X1, X2) -> n__zWquot(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__zWquot(X1, X2)) -> zWquot(X1, X2) [1]
   activate(X) -> X [1]

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

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

(30)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   from(X) -> cons(X, n__from(s(X))) [1]
   sel(0, cons(X, XS)) -> X [1]
   sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) [1]
   minus(X, 0) -> 0 [1]
   minus(s(X), s(Y)) -> minus(X, Y) [1]
   quot(0, s(Y)) -> 0 [1]
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) [1]
   zWquot(XS, nil) -> nil [1]
   zWquot(nil, XS) -> nil [1]
   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) [1]
   from(X) -> n__from(X) [1]
   zWquot(X1, X2) -> n__zWquot(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__zWquot(X1, X2)) -> zWquot(X1, X2) [1]
   activate(X) -> X [1]

The TRS has the following type information:
from :: s:0 -> n__from:cons:nil:n__zWquot
cons :: s:0 -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
n__from :: s:0 -> n__from:cons:nil:n__zWquot
s :: s:0 -> s:0
sel :: s:0 -> n__from:cons:nil:n__zWquot -> s:0
0 :: s:0
activate :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
minus :: s:0 -> s:0 -> s:0
quot :: s:0 -> s:0 -> s:0
zWquot :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
nil :: n__from:cons:nil:n__zWquot
n__zWquot :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot

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

(31) 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:

   sel_2

(c) The following functions are completely defined:

   minus_2
   activate_1
   from_1
   zWquot_2
   quot_2

Due to the following rules being added:

   minus(v0, v1) -> 0 [0]
   quot(v0, v1) -> 0 [0]

And the following fresh constants: none

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

(32)
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(s(X))) [1]
   sel(0, cons(X, XS)) -> X [1]
   sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) [1]
   minus(X, 0) -> 0 [1]
   minus(s(X), s(Y)) -> minus(X, Y) [1]
   quot(0, s(Y)) -> 0 [1]
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) [1]
   zWquot(XS, nil) -> nil [1]
   zWquot(nil, XS) -> nil [1]
   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) [1]
   from(X) -> n__from(X) [1]
   zWquot(X1, X2) -> n__zWquot(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__zWquot(X1, X2)) -> zWquot(X1, X2) [1]
   activate(X) -> X [1]
   minus(v0, v1) -> 0 [0]
   quot(v0, v1) -> 0 [0]

The TRS has the following type information:
from :: s:0 -> n__from:cons:nil:n__zWquot
cons :: s:0 -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
n__from :: s:0 -> n__from:cons:nil:n__zWquot
s :: s:0 -> s:0
sel :: s:0 -> n__from:cons:nil:n__zWquot -> s:0
0 :: s:0
activate :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
minus :: s:0 -> s:0 -> s:0
quot :: s:0 -> s:0 -> s:0
zWquot :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
nil :: n__from:cons:nil:n__zWquot
n__zWquot :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot

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

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

(34)
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(s(X))) [1]
   sel(0, cons(X, XS)) -> X [1]
   sel(s(N), cons(X, n__from(X'))) -> sel(N, from(X')) [2]
   sel(s(N), cons(X, n__zWquot(X1', X2'))) -> sel(N, zWquot(X1', X2')) [2]
   sel(s(N), cons(X, XS)) -> sel(N, XS) [2]
   minus(X, 0) -> 0 [1]
   minus(s(X), s(Y)) -> minus(X, Y) [1]
   quot(0, s(Y)) -> 0 [1]
   quot(s(X), s(0)) -> s(quot(0, s(0))) [2]
   quot(s(s(X'')), s(s(Y'))) -> s(quot(minus(X'', Y'), s(s(Y')))) [2]
   quot(s(X), s(Y)) -> s(quot(0, s(Y))) [1]
   zWquot(XS, nil) -> nil [1]
   zWquot(nil, XS) -> nil [1]
   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) [1]
   from(X) -> n__from(X) [1]
   zWquot(X1, X2) -> n__zWquot(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__zWquot(X1, X2)) -> zWquot(X1, X2) [1]
   activate(X) -> X [1]
   minus(v0, v1) -> 0 [0]
   quot(v0, v1) -> 0 [0]

The TRS has the following type information:
from :: s:0 -> n__from:cons:nil:n__zWquot
cons :: s:0 -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
n__from :: s:0 -> n__from:cons:nil:n__zWquot
s :: s:0 -> s:0
sel :: s:0 -> n__from:cons:nil:n__zWquot -> s:0
0 :: s:0
activate :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
minus :: s:0 -> s:0 -> s:0
quot :: s:0 -> s:0 -> s:0
zWquot :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
nil :: n__from:cons:nil:n__zWquot
n__zWquot :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot

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

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

   0 => 0
   nil => 0

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

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 1 }-> from(X) :|: z = 1 + X, X >= 0
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X + (1 + (1 + X)) :|: X >= 0, z = X
   minus(z, z') -{ 1 }-> minus(X, Y) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0
   minus(z, z') -{ 1 }-> 0 :|: X >= 0, z = X, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 1 }-> 0 :|: Y >= 0, z' = 1 + Y, z = 0
   quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 2 }-> 1 + quot(minus(X'', Y'), 1 + (1 + Y')) :|: z' = 1 + (1 + Y'), Y' >= 0, z = 1 + (1 + X''), X'' >= 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + Y) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z = 1 + X, X >= 0, z' = 1 + 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(N, XS) :|: z = 1 + N, z' = 1 + X + XS, X >= 0, XS >= 0, N >= 0
   sel(z, z') -{ 2 }-> sel(N, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, z = 1 + N, X >= 0, z' = 1 + X + (1 + X1' + X2'), N >= 0
   sel(z, z') -{ 2 }-> sel(N, from(X')) :|: z = 1 + N, z' = 1 + X + (1 + X'), X >= 0, X' >= 0, N >= 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = XS, XS >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z' = XS, z = 0, XS >= 0
   zWquot(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0


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

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

   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X + (1 + (1 + X)) :|: X >= 0, z = X

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

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z = 1 + X, X >= 0, X' >= 0, X = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z = 1 + X, X >= 0, X' >= 0, X = X'
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X + (1 + (1 + X)) :|: X >= 0, z = X
   minus(z, z') -{ 1 }-> minus(X, Y) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0
   minus(z, z') -{ 1 }-> 0 :|: X >= 0, z = X, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 1 }-> 0 :|: Y >= 0, z' = 1 + Y, z = 0
   quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 2 }-> 1 + quot(minus(X'', Y'), 1 + (1 + Y')) :|: z' = 1 + (1 + Y'), Y' >= 0, z = 1 + (1 + X''), X'' >= 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + Y) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z = 1 + X, X >= 0, z' = 1 + 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(N, XS) :|: z = 1 + N, z' = 1 + X + XS, X >= 0, XS >= 0, N >= 0
   sel(z, z') -{ 2 }-> sel(N, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, z = 1 + N, X >= 0, z' = 1 + X + (1 + X1' + X2'), N >= 0
   sel(z, z') -{ 3 }-> sel(N, 1 + X'') :|: z = 1 + N, z' = 1 + X + (1 + X'), X >= 0, X' >= 0, N >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(N, 1 + X'' + (1 + (1 + X''))) :|: z = 1 + N, z' = 1 + X + (1 + X'), X >= 0, X' >= 0, N >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z = XS, XS >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z' = XS, z = 0, XS >= 0
   zWquot(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0


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

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

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 2 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0


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

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

   { from }
   { minus }
   { quot }
   { zWquot, activate }
   { sel }

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

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 2 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {from}, {minus}, {quot}, {zWquot,activate}, {sel}

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 2 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {from}, {minus}, {quot}, {zWquot,activate}, {sel}

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

(45) 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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 2 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {from}, {minus}, {quot}, {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: ?, size: O(n^1) [3 + 2*z]

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

(47) 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: 1

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 2 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {minus}, {quot}, {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 2 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {minus}, {quot}, {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]

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

(51) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 2 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {minus}, {quot}, {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: ?, size: O(1) [0]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 2 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {quot}, {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 + z' }-> s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 + z' }-> 1 + quot(s', 1 + (1 + (z' - 2))) :|: s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {quot}, {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]

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

(57) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 + z' }-> s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 + z' }-> 1 + quot(s', 1 + (1 + (z' - 2))) :|: s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {quot}, {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]
  quot: runtime: ?, size: O(1) [1]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 + z' }-> s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 + z' }-> 1 + quot(s', 1 + (1 + (z' - 2))) :|: s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 2 }-> 1 + quot(0, 1 + 0) :|: z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 1 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Function symbols to be analyzed: {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]
  quot: runtime: O(n^1) [3 + z'], size: O(1) [1]

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

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 + z' }-> s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 6 }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 4 + 2*z' }-> 1 + s1 :|: s1 >= 0, s1 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 4 + z' }-> 1 + s2 :|: s2 >= 0, s2 <= 1, z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 4 + Y }-> 1 + s3 + (1 + activate(XS) + activate(YS)) :|: s3 >= 0, s3 <= 1, z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]
  quot: runtime: O(n^1) [3 + z'], size: O(1) [1]

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

(63) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: zWquot
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2

Computed SIZE bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 12 + 32*z + 24*z^2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 + z' }-> s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 6 }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 4 + 2*z' }-> 1 + s1 :|: s1 >= 0, s1 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 4 + z' }-> 1 + s2 :|: s2 >= 0, s2 <= 1, z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 4 + Y }-> 1 + s3 + (1 + activate(XS) + activate(YS)) :|: s3 >= 0, s3 <= 1, z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {zWquot,activate}, {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]
  quot: runtime: O(n^1) [3 + z'], size: O(1) [1]
  zWquot: runtime: ?, size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: ?, size: O(n^2) [12 + 32*z + 24*z^2]

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: zWquot
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 11 + 12*z + 2*z*z' + z^2 + 12*z' + z'^2

Computed RUNTIME bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 15 + 24*z + 4*z^2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 + z' }-> s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 6 }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 4 + 2*z' }-> 1 + s1 :|: s1 >= 0, s1 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 4 + z' }-> 1 + s2 :|: s2 >= 0, s2 <= 1, z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, zWquot(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 4 + Y }-> 1 + s3 + (1 + activate(XS) + activate(YS)) :|: s3 >= 0, s3 <= 1, z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]
  quot: runtime: O(n^1) [3 + z'], size: O(1) [1]
  zWquot: runtime: O(n^2) [11 + 12*z + 2*z*z' + z^2 + 12*z' + z'^2], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(n^2) [15 + 24*z + 4*z^2], size: O(n^2) [12 + 32*z + 24*z^2]

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

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

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

   activate(z) -{ 12 + 12*X1 + 2*X1*X2 + X1^2 + 12*X2 + X2^2 }-> s7 :|: s7 >= 0, s7 <= 14 * X1 + 14 * X2 + 6 * (X1 * X1) + 12 * (X2 * X1) + 6 * (X2 * X2) + 8, X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 + z' }-> s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 6 }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 4 + 2*z' }-> 1 + s1 :|: s1 >= 0, s1 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 4 + z' }-> 1 + s2 :|: s2 >= 0, s2 <= 1, z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 13 + 12*X1' + 2*X1'*X2' + X1'^2 + 12*X2' + X2'^2 }-> sel(z - 1, s4) :|: s4 >= 0, s4 <= 14 * X1' + 14 * X2' + 6 * (X1' * X1') + 12 * (X2' * X1') + 6 * (X2' * X2') + 8, X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 34 + 24*XS + 4*XS^2 + Y + 24*YS + 4*YS^2 }-> 1 + s3 + (1 + s5 + s6) :|: s5 >= 0, s5 <= 32 * XS + 24 * (XS * XS) + 12, s6 >= 0, s6 <= 32 * YS + 24 * (YS * YS) + 12, s3 >= 0, s3 <= 1, z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]
  quot: runtime: O(n^1) [3 + z'], size: O(1) [1]
  zWquot: runtime: O(n^2) [11 + 12*z + 2*z*z' + z^2 + 12*z' + z'^2], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(n^2) [15 + 24*z + 4*z^2], size: O(n^2) [12 + 32*z + 24*z^2]

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

(69) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 12 + 12*X1 + 2*X1*X2 + X1^2 + 12*X2 + X2^2 }-> s7 :|: s7 >= 0, s7 <= 14 * X1 + 14 * X2 + 6 * (X1 * X1) + 12 * (X2 * X1) + 6 * (X2 * X2) + 8, X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 + z' }-> s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 6 }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 4 + 2*z' }-> 1 + s1 :|: s1 >= 0, s1 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 4 + z' }-> 1 + s2 :|: s2 >= 0, s2 <= 1, z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 13 + 12*X1' + 2*X1'*X2' + X1'^2 + 12*X2' + X2'^2 }-> sel(z - 1, s4) :|: s4 >= 0, s4 <= 14 * X1' + 14 * X2' + 6 * (X1' * X1') + 12 * (X2' * X1') + 6 * (X2' * X2') + 8, X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 34 + 24*XS + 4*XS^2 + Y + 24*YS + 4*YS^2 }-> 1 + s3 + (1 + s5 + s6) :|: s5 >= 0, s5 <= 32 * XS + 24 * (XS * XS) + 12, s6 >= 0, s6 <= 32 * YS + 24 * (YS * YS) + 12, s3 >= 0, s3 <= 1, z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]
  quot: runtime: O(n^1) [3 + z'], size: O(1) [1]
  zWquot: runtime: O(n^2) [11 + 12*z + 2*z*z' + z^2 + 12*z' + z'^2], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(n^2) [15 + 24*z + 4*z^2], size: O(n^2) [12 + 32*z + 24*z^2]
  sel: runtime: ?, size: INF

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

(71) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   activate(z) -{ 12 + 12*X1 + 2*X1*X2 + X1^2 + 12*X2 + X2^2 }-> s7 :|: s7 >= 0, s7 <= 14 * X1 + 14 * X2 + 6 * (X1 * X1) + 12 * (X2 * X1) + 6 * (X2 * X2) + 8, X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X' + (1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 1 + z' }-> s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 6 }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z - 1 >= 0, z' = 1 + 0
   quot(z, z') -{ 4 + 2*z' }-> 1 + s1 :|: s1 >= 0, s1 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 4 + z' }-> 1 + s2 :|: s2 >= 0, s2 <= 1, z' - 1 >= 0, z - 1 >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 2 }-> sel(z - 1, XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0
   sel(z, z') -{ 13 + 12*X1' + 2*X1'*X2' + X1'^2 + 12*X2' + X2'^2 }-> sel(z - 1, s4) :|: s4 >= 0, s4 <= 14 * X1' + 14 * X2' + 6 * (X1' * X1') + 12 * (X2' * X1') + 6 * (X2' * X2') + 8, X2' >= 0, X1' >= 0, X >= 0, z' = 1 + X + (1 + X1' + X2'), z - 1 >= 0
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'') :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   sel(z, z') -{ 3 }-> sel(z - 1, 1 + X'' + (1 + (1 + X''))) :|: z' = 1 + X + (1 + X'), X >= 0, X' >= 0, z - 1 >= 0, X'' >= 0, X' = X''
   zWquot(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z = 0, z' >= 0
   zWquot(z, z') -{ 34 + 24*XS + 4*XS^2 + Y + 24*YS + 4*YS^2 }-> 1 + s3 + (1 + s5 + s6) :|: s5 >= 0, s5 <= 32 * XS + 24 * (XS * XS) + 12, s6 >= 0, s6 <= 32 * YS + 24 * (YS * YS) + 12, s3 >= 0, s3 <= 1, z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0
   zWquot(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0

Function symbols to be analyzed: {sel}
Previous analysis results are:
  from: runtime: O(1) [1], size: O(n^1) [3 + 2*z]
  minus: runtime: O(n^1) [1 + z'], size: O(1) [0]
  quot: runtime: O(n^1) [3 + z'], size: O(1) [1]
  zWquot: runtime: O(n^2) [11 + 12*z + 2*z*z' + z^2 + 12*z' + z'^2], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(n^2) [15 + 24*z + 4*z^2], size: O(n^2) [12 + 32*z + 24*z^2]
  sel: runtime: INF, size: INF

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

(73) 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:

   sel(v0, v1) -> null_sel [0]
   minus(v0, v1) -> null_minus [0]
   quot(v0, v1) -> null_quot [0]

And the following fresh constants:    null_sel, null_minus, null_quot

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

(74)
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(s(X))) [1]
   sel(0, cons(X, XS)) -> X [1]
   sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) [1]
   minus(X, 0) -> 0 [1]
   minus(s(X), s(Y)) -> minus(X, Y) [1]
   quot(0, s(Y)) -> 0 [1]
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) [1]
   zWquot(XS, nil) -> nil [1]
   zWquot(nil, XS) -> nil [1]
   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) [1]
   from(X) -> n__from(X) [1]
   zWquot(X1, X2) -> n__zWquot(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__zWquot(X1, X2)) -> zWquot(X1, X2) [1]
   activate(X) -> X [1]
   sel(v0, v1) -> null_sel [0]
   minus(v0, v1) -> null_minus [0]
   quot(v0, v1) -> null_quot [0]

The TRS has the following type information:
from :: s:0:null_sel:null_minus:null_quot -> n__from:cons:nil:n__zWquot
cons :: s:0:null_sel:null_minus:null_quot -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
n__from :: s:0:null_sel:null_minus:null_quot -> n__from:cons:nil:n__zWquot
s :: s:0:null_sel:null_minus:null_quot -> s:0:null_sel:null_minus:null_quot
sel :: s:0:null_sel:null_minus:null_quot -> n__from:cons:nil:n__zWquot -> s:0:null_sel:null_minus:null_quot
0 :: s:0:null_sel:null_minus:null_quot
activate :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
minus :: s:0:null_sel:null_minus:null_quot -> s:0:null_sel:null_minus:null_quot -> s:0:null_sel:null_minus:null_quot
quot :: s:0:null_sel:null_minus:null_quot -> s:0:null_sel:null_minus:null_quot -> s:0:null_sel:null_minus:null_quot
zWquot :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
nil :: n__from:cons:nil:n__zWquot
n__zWquot :: n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot -> n__from:cons:nil:n__zWquot
null_sel :: s:0:null_sel:null_minus:null_quot
null_minus :: s:0:null_sel:null_minus:null_quot
null_quot :: s:0:null_sel:null_minus:null_quot

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

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

   0 => 0
   nil => 0
   null_sel => 0
   null_minus => 0
   null_quot => 0

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

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

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> zWquot(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 1 }-> from(X) :|: z = 1 + X, X >= 0
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X + (1 + (1 + X)) :|: X >= 0, z = X
   minus(z, z') -{ 1 }-> minus(X, Y) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0
   minus(z, z') -{ 1 }-> 0 :|: X >= 0, z = X, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 1 }-> 0 :|: Y >= 0, z' = 1 + Y, z = 0
   quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 1 }-> 1 + quot(minus(X, Y), 1 + Y) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0
   sel(z, z') -{ 1 }-> X :|: z' = 1 + X + XS, X >= 0, z = 0, XS >= 0
   sel(z, z') -{ 1 }-> sel(N, activate(XS)) :|: z = 1 + N, z' = 1 + X + XS, X >= 0, XS >= 0, N >= 0
   sel(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   zWquot(z, z') -{ 1 }-> 0 :|: z = XS, XS >= 0, z' = 0
   zWquot(z, z') -{ 1 }-> 0 :|: z' = XS, z = 0, XS >= 0
   zWquot(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   zWquot(z, z') -{ 1 }-> 1 + quot(X, Y) + (1 + activate(XS) + activate(YS)) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0

Only complete derivations are relevant for the runtime complexity.

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

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   sel(0, cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
Tuples:
   FROM(z0) -> c
   FROM(z0) -> c1
   SEL(0, cons(z0, z1)) -> c2
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(z0, 0) -> c4
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(0, s(z0)) -> c6
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(z0, nil) -> c8
   ZWQUOT(nil, z0) -> c9
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ZWQUOT(z0, z1) -> c13
   ACTIVATE(n__from(z0)) -> c14(FROM(z0))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ACTIVATE(z0) -> c16
S tuples:
   FROM(z0) -> c
   FROM(z0) -> c1
   SEL(0, cons(z0, z1)) -> c2
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(z0, 0) -> c4
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(0, s(z0)) -> c6
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(z0, nil) -> c8
   ZWQUOT(nil, z0) -> c9
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ZWQUOT(z0, z1) -> c13
   ACTIVATE(n__from(z0)) -> c14(FROM(z0))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ACTIVATE(z0) -> c16
K tuples:none
Defined Rule Symbols:   from_1, sel_2, minus_2, quot_2, zWquot_2, activate_1

Defined Pair Symbols:   FROM_1, SEL_2, MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c, c1, c2, c3_2, c4, c5_1, c6, c7_2, c8, c9, c10_1, c11_1, c12_1, c13, c14_1, c15_1, c16


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

(79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   QUOT(0, s(z0)) -> c6
   ZWQUOT(nil, z0) -> c9
   MINUS(z0, 0) -> c4
   ACTIVATE(n__from(z0)) -> c14(FROM(z0))
   ZWQUOT(z0, z1) -> c13
   ZWQUOT(z0, nil) -> c8
   FROM(z0) -> c1
   FROM(z0) -> c
   ACTIVATE(z0) -> c16
   SEL(0, cons(z0, z1)) -> c2

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   sel(0, cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
Tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
S tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
K tuples:none
Defined Rule Symbols:   from_1, sel_2, minus_2, quot_2, zWquot_2, activate_1

Defined Pair Symbols:   SEL_2, MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c5_1, c7_2, c10_1, c11_1, c12_1, c15_1


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

(81) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   sel(0, cons(z0, z1)) -> z0
   sel(s(z0), cons(z1, z2)) -> sel(z0, activate(z2))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
S tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c5_1, c7_2, c10_1, c11_1, c12_1, c15_1


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

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

(84)
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:

   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))

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

   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)

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

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

(86)
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:

   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)

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

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

(88)
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:

   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2)) [1]
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1)) [1]
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3)) [1]
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1)) [1]
   activate(n__from(z0)) -> from(z0) [0]
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   zWquot(z0, nil) -> nil [0]
   zWquot(nil, z0) -> nil [0]
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3))) [0]
   zWquot(z0, z1) -> n__zWquot(z0, z1) [0]
   quot(0, s(z0)) -> 0 [0]
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1))) [0]
   minus(z0, 0) -> 0 [0]
   minus(s(z0), s(z1)) -> minus(z0, z1) [0]

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

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

(90)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2)) [1]
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1)) [1]
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3)) [1]
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1)) [1]
   activate(n__from(z0)) -> from(z0) [0]
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   zWquot(z0, nil) -> nil [0]
   zWquot(nil, z0) -> nil [0]
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3))) [0]
   zWquot(z0, z1) -> n__zWquot(z0, z1) [0]
   quot(0, s(z0)) -> 0 [0]
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1))) [0]
   minus(z0, 0) -> 0 [0]
   minus(s(z0), s(z1)) -> minus(z0, z1) [0]

The TRS has the following type information:
SEL :: s:0 -> cons:n__zWquot:n__from:nil -> c3
s :: s:0 -> s:0
cons :: s:0 -> cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
c3 :: c3 -> c15 -> c3
activate :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
ACTIVATE :: cons:n__zWquot:n__from:nil -> c15
MINUS :: s:0 -> s:0 -> c5
c5 :: c5 -> c5
QUOT :: s:0 -> s:0 -> c7
c7 :: c7 -> c5 -> c7
minus :: s:0 -> s:0 -> s:0
ZWQUOT :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil -> c10:c11:c12
c10 :: c7 -> c10:c11:c12
c11 :: c15 -> c10:c11:c12
c12 :: c15 -> c10:c11:c12
n__zWquot :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
c15 :: c10:c11:c12 -> c15
n__from :: s:0 -> cons:n__zWquot:n__from:nil
from :: s:0 -> cons:n__zWquot:n__from:nil
zWquot :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
nil :: cons:n__zWquot:n__from:nil
quot :: s:0 -> s:0 -> s:0
0 :: s:0

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

(91) 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:

   SEL_2
   MINUS_2
   QUOT_2
   ZWQUOT_2
   ACTIVATE_1

(c) The following functions are completely defined:

   activate_1
   from_1
   zWquot_2
   quot_2
   minus_2

Due to the following rules being added:

   activate(v0) -> nil [0]
   from(v0) -> nil [0]
   zWquot(v0, v1) -> nil [0]
   quot(v0, v1) -> 0 [0]
   minus(v0, v1) -> 0 [0]

And the following fresh constants:    const, const1, const2, const3, const4

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

(92)
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:

   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2)) [1]
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1)) [1]
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3)) [1]
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1)) [1]
   activate(n__from(z0)) -> from(z0) [0]
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   zWquot(z0, nil) -> nil [0]
   zWquot(nil, z0) -> nil [0]
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3))) [0]
   zWquot(z0, z1) -> n__zWquot(z0, z1) [0]
   quot(0, s(z0)) -> 0 [0]
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1))) [0]
   minus(z0, 0) -> 0 [0]
   minus(s(z0), s(z1)) -> minus(z0, z1) [0]
   activate(v0) -> nil [0]
   from(v0) -> nil [0]
   zWquot(v0, v1) -> nil [0]
   quot(v0, v1) -> 0 [0]
   minus(v0, v1) -> 0 [0]

The TRS has the following type information:
SEL :: s:0 -> cons:n__zWquot:n__from:nil -> c3
s :: s:0 -> s:0
cons :: s:0 -> cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
c3 :: c3 -> c15 -> c3
activate :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
ACTIVATE :: cons:n__zWquot:n__from:nil -> c15
MINUS :: s:0 -> s:0 -> c5
c5 :: c5 -> c5
QUOT :: s:0 -> s:0 -> c7
c7 :: c7 -> c5 -> c7
minus :: s:0 -> s:0 -> s:0
ZWQUOT :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil -> c10:c11:c12
c10 :: c7 -> c10:c11:c12
c11 :: c15 -> c10:c11:c12
c12 :: c15 -> c10:c11:c12
n__zWquot :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
c15 :: c10:c11:c12 -> c15
n__from :: s:0 -> cons:n__zWquot:n__from:nil
from :: s:0 -> cons:n__zWquot:n__from:nil
zWquot :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
nil :: cons:n__zWquot:n__from:nil
quot :: s:0 -> s:0 -> s:0
0 :: s:0
const :: c3
const1 :: c15
const2 :: c5
const3 :: c7
const4 :: c10:c11:c12

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

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

(94)
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:

   SEL(s(z0), cons(z1, n__from(z0'))) -> c3(SEL(z0, from(z0')), ACTIVATE(n__from(z0'))) [1]
   SEL(s(z0), cons(z1, n__zWquot(z0'', z1'))) -> c3(SEL(z0, zWquot(z0'', z1')), ACTIVATE(n__zWquot(z0'', z1'))) [1]
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, z2), ACTIVATE(z2)) [1]
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, nil), ACTIVATE(z2)) [1]
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1)) [1]
   QUOT(s(z0), s(0)) -> c7(QUOT(0, s(0)), MINUS(z0, 0)) [1]
   QUOT(s(s(z01)), s(s(z1''))) -> c7(QUOT(minus(z01, z1''), s(s(z1''))), MINUS(s(z01), s(z1''))) [1]
   QUOT(s(z0), s(z1)) -> c7(QUOT(0, s(z1)), MINUS(z0, z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3)) [1]
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1)) [1]
   activate(n__from(z0)) -> from(z0) [0]
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   zWquot(z0, nil) -> nil [0]
   zWquot(nil, z0) -> nil [0]
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3))) [0]
   zWquot(z0, z1) -> n__zWquot(z0, z1) [0]
   quot(0, s(z0)) -> 0 [0]
   quot(s(z0), s(0)) -> s(quot(0, s(0))) [0]
   quot(s(s(z02)), s(s(z11))) -> s(quot(minus(z02, z11), s(s(z11)))) [0]
   quot(s(z0), s(z1)) -> s(quot(0, s(z1))) [0]
   minus(z0, 0) -> 0 [0]
   minus(s(z0), s(z1)) -> minus(z0, z1) [0]
   activate(v0) -> nil [0]
   from(v0) -> nil [0]
   zWquot(v0, v1) -> nil [0]
   quot(v0, v1) -> 0 [0]
   minus(v0, v1) -> 0 [0]

The TRS has the following type information:
SEL :: s:0 -> cons:n__zWquot:n__from:nil -> c3
s :: s:0 -> s:0
cons :: s:0 -> cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
c3 :: c3 -> c15 -> c3
activate :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
ACTIVATE :: cons:n__zWquot:n__from:nil -> c15
MINUS :: s:0 -> s:0 -> c5
c5 :: c5 -> c5
QUOT :: s:0 -> s:0 -> c7
c7 :: c7 -> c5 -> c7
minus :: s:0 -> s:0 -> s:0
ZWQUOT :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil -> c10:c11:c12
c10 :: c7 -> c10:c11:c12
c11 :: c15 -> c10:c11:c12
c12 :: c15 -> c10:c11:c12
n__zWquot :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
c15 :: c10:c11:c12 -> c15
n__from :: s:0 -> cons:n__zWquot:n__from:nil
from :: s:0 -> cons:n__zWquot:n__from:nil
zWquot :: cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil -> cons:n__zWquot:n__from:nil
nil :: cons:n__zWquot:n__from:nil
quot :: s:0 -> s:0 -> s:0
0 :: s:0
const :: c3
const1 :: c15
const2 :: c5
const3 :: c7
const4 :: c10:c11:c12

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:

   nil => 0
   0 => 0
   const => 0
   const1 => 0
   const2 => 0
   const3 => 0
   const4 => 0

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

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

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z01, z1''), 1 + (1 + z1'')) + MINUS(1 + z01, 1 + z1'') :|: z = 1 + (1 + z01), z' = 1 + (1 + z1''), z01 >= 0, z1'' >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + z1) + MINUS(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z0, 0) :|: z = 1 + z0, z' = 1 + 0, z0 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z = 1 + z0, z1' >= 0, z0 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, from(z0')) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z = 1 + z0, z0 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> from(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   from(z) -{ 0 }-> 1 + z0 + (1 + (1 + z0)) :|: z = z0, z0 >= 0
   minus(z, z') -{ 0 }-> minus(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   minus(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 0 }-> 0 :|: z0 >= 0, z' = 1 + z0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 0 }-> 1 + quot(minus(z02, z11), 1 + (1 + z11)) :|: z = 1 + (1 + z02), z11 >= 0, z02 >= 0, z' = 1 + (1 + z11)
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z = 1 + z0, z' = 1 + 0, z0 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z0 >= 0, z = 0, z' = z0
   zWquot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   zWquot(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0


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

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

   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   from(z) -{ 0 }-> 1 + z0 + (1 + (1 + z0)) :|: z = z0, z0 >= 0

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

(98)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z01, z1''), 1 + (1 + z1'')) + MINUS(1 + z01, 1 + z1'') :|: z = 1 + (1 + z01), z' = 1 + (1 + z1''), z01 >= 0, z1'' >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + z1) + MINUS(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z0, 0) :|: z = 1 + z0, z' = 1 + 0, z0 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z = 1 + z0, z1' >= 0, z0 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z = 1 + z0, z0 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z = 1 + z0, z0 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z = 1 + z0, z0 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   activate(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, z0 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, z0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z = 1 + z0, z0 >= 0, z0 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   from(z) -{ 0 }-> 1 + z0 + (1 + (1 + z0)) :|: z = z0, z0 >= 0
   minus(z, z') -{ 0 }-> minus(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   minus(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 0 }-> 0 :|: z0 >= 0, z' = 1 + z0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 0 }-> 1 + quot(minus(z02, z11), 1 + (1 + z11)) :|: z = 1 + (1 + z02), z11 >= 0, z02 >= 0, z' = 1 + (1 + z11)
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z = 1 + z0, z' = 1 + 0, z0 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z0 >= 0, z = 0, z' = z0
   zWquot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   zWquot(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0


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

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

(100)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0


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

   { from }
   { minus }
   { MINUS }
   { quot }
   { QUOT }
   { zWquot, activate }
   { ZWQUOT, ACTIVATE }
   { SEL }

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

(102)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {from}, {minus}, {MINUS}, {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}

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

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

(104)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {from}, {minus}, {MINUS}, {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}

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

(105) 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

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

(106)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {from}, {minus}, {MINUS}, {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: ?, size: O(n^1) [3 + 2*z]

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

(107) 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

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

(108)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {minus}, {MINUS}, {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]

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

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

(110)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {minus}, {MINUS}, {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]

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

(111) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(112)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {minus}, {MINUS}, {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: ?, size: O(1) [0]

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

(113) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(114)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> minus(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(minus(z - 2, z' - 2), 1 + (1 + (z' - 2))) :|: z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {MINUS}, {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]

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

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

(116)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(s, 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(s', 1 + (1 + (z' - 2))) :|: s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {MINUS}, {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]

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

(117) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(118)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(s, 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(s', 1 + (1 + (z' - 2))) :|: s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {MINUS}, {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: ?, size: O(1) [0]

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

(119) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(120)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(s, 1 + (1 + (z' - 2))) + MINUS(1 + (z - 2), 1 + (z' - 2)) :|: s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + MINUS(z - 1, 0) :|: z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + (z' - 1)) + MINUS(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(s', 1 + (1 + (z' - 2))) :|: s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]

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

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

(122)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(s, 1 + (1 + (z' - 2))) + s3 :|: s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + s2 :|: s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(0, 1 + (z' - 1)) + s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(s', 1 + (1 + (z' - 2))) :|: s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]

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

(123) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(124)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(s, 1 + (1 + (z' - 2))) + s3 :|: s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + s2 :|: s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(0, 1 + (z' - 1)) + s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(s', 1 + (1 + (z' - 2))) :|: s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {quot}, {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: ?, size: O(1) [1]

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

(125) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(126)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(s, 1 + (1 + (z' - 2))) + s3 :|: s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + s2 :|: s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(0, 1 + (z' - 1)) + s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + quot(s', 1 + (1 + (z' - 2))) :|: s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + 0) :|: z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + quot(0, 1 + (z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Function symbols to be analyzed: {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]

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

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

(128)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(s, 1 + (1 + (z' - 2))) + s3 :|: s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + s2 :|: s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(0, 1 + (z' - 1)) + s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + activate(z1) + activate(z3)) :|: s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]

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

(129) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(130)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(s, 1 + (1 + (z' - 2))) + s3 :|: s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + s2 :|: s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(0, 1 + (z' - 1)) + s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + activate(z1) + activate(z3)) :|: s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {QUOT}, {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: ?, size: O(1) [0]

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

(131) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(132)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(s, 1 + (1 + (z' - 2))) + s3 :|: s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 }-> 1 + QUOT(0, 1 + 0) + s2 :|: s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   QUOT(z, z') -{ z' }-> 1 + QUOT(0, 1 + (z' - 1)) + s4 :|: s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + activate(z1) + activate(z3)) :|: s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]

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

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

(134)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s10 + s3 :|: s10 >= 0, s10 <= 0, s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s11 + s4 :|: s11 >= 0, s11 <= 0, s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 3 }-> 1 + s9 + s2 :|: s9 >= 0, s9 <= 0, s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 2 + z2 }-> 1 + s12 :|: s12 >= 0, s12 <= 0, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + activate(z1) + activate(z3)) :|: s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]

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

(135) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: zWquot
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2

Computed SIZE bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 12 + 32*z + 24*z^2

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

(136)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s10 + s3 :|: s10 >= 0, s10 <= 0, s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s11 + s4 :|: s11 >= 0, s11 <= 0, s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 3 }-> 1 + s9 + s2 :|: s9 >= 0, s9 <= 0, s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 2 + z2 }-> 1 + s12 :|: s12 >= 0, s12 <= 0, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + activate(z1) + activate(z3)) :|: s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {zWquot,activate}, {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]
  zWquot: runtime: ?, size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: ?, size: O(n^2) [12 + 32*z + 24*z^2]

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

(137) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

(138)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s10 + s3 :|: s10 >= 0, s10 <= 0, s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s11 + s4 :|: s11 >= 0, s11 <= 0, s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 3 }-> 1 + s9 + s2 :|: s9 >= 0, s9 <= 0, s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, zWquot(z0'', z1')) + ACTIVATE(1 + z0'' + z1') :|: z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 2 + z2 }-> 1 + s12 :|: s12 >= 0, s12 <= 0, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + activate(z1) + activate(z3)) :|: s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]
  zWquot: runtime: O(1) [0], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(1) [0], size: O(n^2) [12 + 32*z + 24*z^2]

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

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

(140)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s10 + s3 :|: s10 >= 0, s10 <= 0, s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s11 + s4 :|: s11 >= 0, s11 <= 0, s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 3 }-> 1 + s9 + s2 :|: s9 >= 0, s9 <= 0, s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s13) + ACTIVATE(1 + z0'' + z1') :|: s13 >= 0, s13 <= 14 * z0'' + 14 * z1' + 6 * (z0'' * z0'') + 12 * (z1' * z0'') + 6 * (z1' * z1') + 8, z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 2 + z2 }-> 1 + s12 :|: s12 >= 0, s12 <= 0, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> s14 :|: s14 >= 0, s14 <= 14 * z0 + 14 * z1 + 6 * (z0 * z0) + 12 * (z1 * z0) + 6 * (z1 * z1) + 8, z1 >= 0, z0 >= 0, z = 1 + z0 + 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 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + s15 + s16) :|: s15 >= 0, s15 <= 32 * z1 + 24 * (z1 * z1) + 12, s16 >= 0, s16 <= 32 * z3 + 24 * (z3 * z3) + 12, s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]
  zWquot: runtime: O(1) [0], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(1) [0], size: O(n^2) [12 + 32*z + 24*z^2]

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

(141) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

(142)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s10 + s3 :|: s10 >= 0, s10 <= 0, s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s11 + s4 :|: s11 >= 0, s11 <= 0, s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 3 }-> 1 + s9 + s2 :|: s9 >= 0, s9 <= 0, s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s13) + ACTIVATE(1 + z0'' + z1') :|: s13 >= 0, s13 <= 14 * z0'' + 14 * z1' + 6 * (z0'' * z0'') + 12 * (z1' * z0'') + 6 * (z1' * z1') + 8, z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 2 + z2 }-> 1 + s12 :|: s12 >= 0, s12 <= 0, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> s14 :|: s14 >= 0, s14 <= 14 * z0 + 14 * z1 + 6 * (z0 * z0) + 12 * (z1 * z0) + 6 * (z1 * z1) + 8, z1 >= 0, z0 >= 0, z = 1 + z0 + 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 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + s15 + s16) :|: s15 >= 0, s15 <= 32 * z1 + 24 * (z1 * z1) + 12, s16 >= 0, s16 <= 32 * z3 + 24 * (z3 * z3) + 12, s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {ZWQUOT,ACTIVATE}, {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]
  zWquot: runtime: O(1) [0], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(1) [0], size: O(n^2) [12 + 32*z + 24*z^2]
  ZWQUOT: runtime: ?, size: O(n^1) [2*z + 2*z']
  ACTIVATE: runtime: ?, size: O(n^1) [2*z]

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

(143) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: ZWQUOT
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + 2*z + 2*z'

Computed RUNTIME bound using CoFloCo for: ACTIVATE
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4 + 2*z

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

(144)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s10 + s3 :|: s10 >= 0, s10 <= 0, s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s11 + s4 :|: s11 >= 0, s11 <= 0, s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 3 }-> 1 + s9 + s2 :|: s9 >= 0, s9 <= 0, s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, s13) + ACTIVATE(1 + z0'' + z1') :|: s13 >= 0, s13 <= 14 * z0'' + 14 * z1' + 6 * (z0'' * z0'') + 12 * (z1' * z0'') + 6 * (z1' * z1') + 8, z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, z2) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 0) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'') + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 1 }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + ACTIVATE(1 + z0') :|: z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 2 + z2 }-> 1 + s12 :|: s12 >= 0, s12 <= 0, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> s14 :|: s14 >= 0, s14 <= 14 * z0 + 14 * z1 + 6 * (z0 * z0) + 12 * (z1 * z0) + 6 * (z1 * z1) + 8, z1 >= 0, z0 >= 0, z = 1 + z0 + 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 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + s15 + s16) :|: s15 >= 0, s15 <= 32 * z1 + 24 * (z1 * z1) + 12, s16 >= 0, s16 <= 32 * z3 + 24 * (z3 * z3) + 12, s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]
  zWquot: runtime: O(1) [0], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(1) [0], size: O(n^2) [12 + 32*z + 24*z^2]
  ZWQUOT: runtime: O(n^1) [5 + 2*z + 2*z'], size: O(n^1) [2*z + 2*z']
  ACTIVATE: runtime: O(n^1) [4 + 2*z], size: O(n^1) [2*z]

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

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

(146)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 6 + 2*z0 + 2*z1 }-> 1 + s22 :|: s22 >= 0, s22 <= 2 * z0 + 2 * z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s10 + s3 :|: s10 >= 0, s10 <= 0, s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s11 + s4 :|: s11 >= 0, s11 <= 0, s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 3 }-> 1 + s9 + s2 :|: s9 >= 0, s9 <= 0, s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   SEL(z, z') -{ 7 + 2*z0'' + 2*z1' }-> 1 + SEL(z - 1, s13) + s17 :|: s17 >= 0, s17 <= 2 * (1 + z0'' + z1'), s13 >= 0, s13 <= 14 * z0'' + 14 * z1' + 6 * (z0'' * z0'') + 12 * (z1' * z0'') + 6 * (z1' * z1') + 8, z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 5 + 2*z2 }-> 1 + SEL(z - 1, z2) + s18 :|: s18 >= 0, s18 <= 2 * z2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 5 + 2*z2 }-> 1 + SEL(z - 1, 0) + s19 :|: s19 >= 0, s19 <= 2 * z2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 7 + 2*z0' }-> 1 + SEL(z - 1, 0) + s23 :|: s23 >= 0, s23 <= 2 * (1 + z0'), z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 7 + 2*z0' }-> 1 + SEL(z - 1, 1 + z0'') + s24 :|: s24 >= 0, s24 <= 2 * (1 + z0'), z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 7 + 2*z0' }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + s25 :|: s25 >= 0, s25 <= 2 * (1 + z0'), z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 2 + z2 }-> 1 + s12 :|: s12 >= 0, s12 <= 0, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 5 + 2*z1 }-> 1 + s20 :|: s20 >= 0, s20 <= 2 * z1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 5 + 2*z3 }-> 1 + s21 :|: s21 >= 0, s21 <= 2 * z3, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> s14 :|: s14 >= 0, s14 <= 14 * z0 + 14 * z1 + 6 * (z0 * z0) + 12 * (z1 * z0) + 6 * (z1 * z1) + 8, z1 >= 0, z0 >= 0, z = 1 + z0 + 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 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + s15 + s16) :|: s15 >= 0, s15 <= 32 * z1 + 24 * (z1 * z1) + 12, s16 >= 0, s16 <= 32 * z3 + 24 * (z3 * z3) + 12, s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]
  zWquot: runtime: O(1) [0], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(1) [0], size: O(n^2) [12 + 32*z + 24*z^2]
  ZWQUOT: runtime: O(n^1) [5 + 2*z + 2*z'], size: O(n^1) [2*z + 2*z']
  ACTIVATE: runtime: O(n^1) [4 + 2*z], size: O(n^1) [2*z]

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

(147) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(148)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 6 + 2*z0 + 2*z1 }-> 1 + s22 :|: s22 >= 0, s22 <= 2 * z0 + 2 * z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s10 + s3 :|: s10 >= 0, s10 <= 0, s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s11 + s4 :|: s11 >= 0, s11 <= 0, s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 3 }-> 1 + s9 + s2 :|: s9 >= 0, s9 <= 0, s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   SEL(z, z') -{ 7 + 2*z0'' + 2*z1' }-> 1 + SEL(z - 1, s13) + s17 :|: s17 >= 0, s17 <= 2 * (1 + z0'' + z1'), s13 >= 0, s13 <= 14 * z0'' + 14 * z1' + 6 * (z0'' * z0'') + 12 * (z1' * z0'') + 6 * (z1' * z1') + 8, z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 5 + 2*z2 }-> 1 + SEL(z - 1, z2) + s18 :|: s18 >= 0, s18 <= 2 * z2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 5 + 2*z2 }-> 1 + SEL(z - 1, 0) + s19 :|: s19 >= 0, s19 <= 2 * z2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 7 + 2*z0' }-> 1 + SEL(z - 1, 0) + s23 :|: s23 >= 0, s23 <= 2 * (1 + z0'), z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 7 + 2*z0' }-> 1 + SEL(z - 1, 1 + z0'') + s24 :|: s24 >= 0, s24 <= 2 * (1 + z0'), z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 7 + 2*z0' }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + s25 :|: s25 >= 0, s25 <= 2 * (1 + z0'), z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 2 + z2 }-> 1 + s12 :|: s12 >= 0, s12 <= 0, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 5 + 2*z1 }-> 1 + s20 :|: s20 >= 0, s20 <= 2 * z1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 5 + 2*z3 }-> 1 + s21 :|: s21 >= 0, s21 <= 2 * z3, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> s14 :|: s14 >= 0, s14 <= 14 * z0 + 14 * z1 + 6 * (z0 * z0) + 12 * (z1 * z0) + 6 * (z1 * z1) + 8, z1 >= 0, z0 >= 0, z = 1 + z0 + 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 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + s15 + s16) :|: s15 >= 0, s15 <= 32 * z1 + 24 * (z1 * z1) + 12, s16 >= 0, s16 <= 32 * z3 + 24 * (z3 * z3) + 12, s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]
  zWquot: runtime: O(1) [0], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(1) [0], size: O(n^2) [12 + 32*z + 24*z^2]
  ZWQUOT: runtime: O(n^1) [5 + 2*z + 2*z'], size: O(n^1) [2*z + 2*z']
  ACTIVATE: runtime: O(n^1) [4 + 2*z], size: O(n^1) [2*z]
  SEL: runtime: ?, size: O(1) [0]

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

(149) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(150)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 6 + 2*z0 + 2*z1 }-> 1 + s22 :|: s22 >= 0, s22 <= 2 * z0 + 2 * z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ z' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s10 + s3 :|: s10 >= 0, s10 <= 0, s3 >= 0, s3 <= 0, s >= 0, s <= 0, z - 2 >= 0, z' - 2 >= 0
   QUOT(z, z') -{ 1 + 2*z' }-> 1 + s11 + s4 :|: s11 >= 0, s11 <= 0, s4 >= 0, s4 <= 0, z' - 1 >= 0, z - 1 >= 0
   QUOT(z, z') -{ 3 }-> 1 + s9 + s2 :|: s9 >= 0, s9 <= 0, s2 >= 0, s2 <= 0, z' = 1 + 0, z - 1 >= 0
   SEL(z, z') -{ 7 + 2*z0'' + 2*z1' }-> 1 + SEL(z - 1, s13) + s17 :|: s17 >= 0, s17 <= 2 * (1 + z0'' + z1'), s13 >= 0, s13 <= 14 * z0'' + 14 * z1' + 6 * (z0'' * z0'') + 12 * (z1' * z0'') + 6 * (z1' * z1') + 8, z1 >= 0, z1' >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z0'' + z1'), z0'' >= 0
   SEL(z, z') -{ 5 + 2*z2 }-> 1 + SEL(z - 1, z2) + s18 :|: s18 >= 0, s18 <= 2 * z2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 5 + 2*z2 }-> 1 + SEL(z - 1, 0) + s19 :|: s19 >= 0, s19 <= 2 * z2, z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0
   SEL(z, z') -{ 7 + 2*z0' }-> 1 + SEL(z - 1, 0) + s23 :|: s23 >= 0, s23 <= 2 * (1 + z0'), z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, v0 >= 0, z0' = v0
   SEL(z, z') -{ 7 + 2*z0' }-> 1 + SEL(z - 1, 1 + z0'') + s24 :|: s24 >= 0, s24 <= 2 * (1 + z0'), z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   SEL(z, z') -{ 7 + 2*z0' }-> 1 + SEL(z - 1, 1 + z0'' + (1 + (1 + z0''))) + s25 :|: s25 >= 0, s25 <= 2 * (1 + z0'), z' = 1 + z1 + (1 + z0'), z1 >= 0, z0' >= 0, z - 1 >= 0, z0' = z0'', z0'' >= 0
   ZWQUOT(z, z') -{ 2 + z2 }-> 1 + s12 :|: s12 >= 0, s12 <= 0, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 5 + 2*z1 }-> 1 + s20 :|: s20 >= 0, s20 <= 2 * z1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 5 + 2*z3 }-> 1 + s21 :|: s21 >= 0, s21 <= 2 * z3, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> s14 :|: s14 >= 0, s14 <= 14 * z0 + 14 * z1 + 6 * (z0 * z0) + 12 * (z1 * z0) + 6 * (z1 * z1) + 8, z1 >= 0, z0 >= 0, z = 1 + z0 + 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 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0
   minus(z, z') -{ 0 }-> s'' :|: s'' >= 0, s'' <= 0, z' - 1 >= 0, z - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   quot(z, z') -{ 0 }-> 1 + s6 :|: s6 >= 0, s6 <= 1, z' = 1 + 0, z - 1 >= 0
   quot(z, z') -{ 0 }-> 1 + s7 :|: s7 >= 0, s7 <= 1, s' >= 0, s' <= 0, z' - 2 >= 0, z - 2 >= 0
   quot(z, z') -{ 0 }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z' - 1 >= 0, z - 1 >= 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   zWquot(z, z') -{ 0 }-> 1 + s5 + (1 + s15 + s16) :|: s15 >= 0, s15 <= 32 * z1 + 24 * (z1 * z1) + 12, s16 >= 0, s16 <= 32 * z3 + 24 * (z3 * z3) + 12, s5 >= 0, s5 <= 1, z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   zWquot(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0

Function symbols to be analyzed: {SEL}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  minus: runtime: O(1) [0], size: O(1) [0]
  MINUS: runtime: O(n^1) [z'], size: O(1) [0]
  quot: runtime: O(1) [0], size: O(1) [1]
  QUOT: runtime: O(n^1) [1 + z'], size: O(1) [0]
  zWquot: runtime: O(1) [0], size: O(n^2) [8 + 14*z + 12*z*z' + 6*z^2 + 14*z' + 6*z'^2]
  activate: runtime: O(1) [0], size: O(n^2) [12 + 32*z + 24*z^2]
  ZWQUOT: runtime: O(n^1) [5 + 2*z + 2*z'], size: O(n^1) [2*z + 2*z']
  ACTIVATE: runtime: O(n^1) [4 + 2*z], size: O(n^1) [2*z]
  SEL: runtime: INF, size: O(1) [0]

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

(151) 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]
   zWquot(v0, v1) -> null_zWquot [0]
   quot(v0, v1) -> null_quot [0]
   minus(v0, v1) -> null_minus [0]
   SEL(v0, v1) -> null_SEL [0]
   MINUS(v0, v1) -> null_MINUS [0]
   QUOT(v0, v1) -> null_QUOT [0]
   ZWQUOT(v0, v1) -> null_ZWQUOT [0]
   ACTIVATE(v0) -> null_ACTIVATE [0]

And the following fresh constants:    null_activate, null_from, null_zWquot, null_quot, null_minus, null_SEL, null_MINUS, null_QUOT, null_ZWQUOT, null_ACTIVATE

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

(152)
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:

   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2)) [1]
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1)) [1]
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1)) [1]
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3)) [1]
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1)) [1]
   activate(n__from(z0)) -> from(z0) [0]
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   zWquot(z0, nil) -> nil [0]
   zWquot(nil, z0) -> nil [0]
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3))) [0]
   zWquot(z0, z1) -> n__zWquot(z0, z1) [0]
   quot(0, s(z0)) -> 0 [0]
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1))) [0]
   minus(z0, 0) -> 0 [0]
   minus(s(z0), s(z1)) -> minus(z0, z1) [0]
   activate(v0) -> null_activate [0]
   from(v0) -> null_from [0]
   zWquot(v0, v1) -> null_zWquot [0]
   quot(v0, v1) -> null_quot [0]
   minus(v0, v1) -> null_minus [0]
   SEL(v0, v1) -> null_SEL [0]
   MINUS(v0, v1) -> null_MINUS [0]
   QUOT(v0, v1) -> null_QUOT [0]
   ZWQUOT(v0, v1) -> null_ZWQUOT [0]
   ACTIVATE(v0) -> null_ACTIVATE [0]

The TRS has the following type information:
SEL :: s:0:null_quot:null_minus -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> c3:null_SEL
s :: s:0:null_quot:null_minus -> s:0:null_quot:null_minus
cons :: s:0:null_quot:null_minus -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
c3 :: c3:null_SEL -> c15:null_ACTIVATE -> c3:null_SEL
activate :: cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
ACTIVATE :: cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> c15:null_ACTIVATE
MINUS :: s:0:null_quot:null_minus -> s:0:null_quot:null_minus -> c5:null_MINUS
c5 :: c5:null_MINUS -> c5:null_MINUS
QUOT :: s:0:null_quot:null_minus -> s:0:null_quot:null_minus -> c7:null_QUOT
c7 :: c7:null_QUOT -> c5:null_MINUS -> c7:null_QUOT
minus :: s:0:null_quot:null_minus -> s:0:null_quot:null_minus -> s:0:null_quot:null_minus
ZWQUOT :: cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> c10:c11:c12:null_ZWQUOT
c10 :: c7:null_QUOT -> c10:c11:c12:null_ZWQUOT
c11 :: c15:null_ACTIVATE -> c10:c11:c12:null_ZWQUOT
c12 :: c15:null_ACTIVATE -> c10:c11:c12:null_ZWQUOT
n__zWquot :: cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
c15 :: c10:c11:c12:null_ZWQUOT -> c15:null_ACTIVATE
n__from :: s:0:null_quot:null_minus -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
from :: s:0:null_quot:null_minus -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
zWquot :: cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot -> cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
nil :: cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
quot :: s:0:null_quot:null_minus -> s:0:null_quot:null_minus -> s:0:null_quot:null_minus
0 :: s:0:null_quot:null_minus
null_activate :: cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
null_from :: cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
null_zWquot :: cons:n__zWquot:n__from:nil:null_activate:null_from:null_zWquot
null_quot :: s:0:null_quot:null_minus
null_minus :: s:0:null_quot:null_minus
null_SEL :: c3:null_SEL
null_MINUS :: c5:null_MINUS
null_QUOT :: c7:null_QUOT
null_ZWQUOT :: c10:c11:c12:null_ZWQUOT
null_ACTIVATE :: c15:null_ACTIVATE

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

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

   nil => 0
   0 => 0
   null_activate => 0
   null_from => 0
   null_zWquot => 0
   null_quot => 0
   null_minus => 0
   null_SEL => 0
   null_MINUS => 0
   null_QUOT => 0
   null_ZWQUOT => 0
   null_ACTIVATE => 0

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

(154)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   ACTIVATE(z) -{ 1 }-> 1 + ZWQUOT(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MINUS(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   MINUS(z, z') -{ 1 }-> 1 + MINUS(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   QUOT(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   QUOT(z, z') -{ 1 }-> 1 + QUOT(minus(z0, z1), 1 + z1) + MINUS(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   SEL(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   SEL(z, z') -{ 1 }-> 1 + SEL(z0, activate(z2)) + ACTIVATE(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   ZWQUOT(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   ZWQUOT(z, z') -{ 1 }-> 1 + QUOT(z0, z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   ZWQUOT(z, z') -{ 1 }-> 1 + ACTIVATE(z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> zWquot(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> from(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   from(z) -{ 0 }-> 1 + z0 + (1 + (1 + z0)) :|: z = z0, z0 >= 0
   minus(z, z') -{ 0 }-> minus(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   minus(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 0 }-> 0 :|: z0 >= 0, z' = 1 + z0, z = 0
   quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   quot(z, z') -{ 0 }-> 1 + quot(minus(z0, z1), 1 + z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   zWquot(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0
   zWquot(z, z') -{ 0 }-> 0 :|: z0 >= 0, z = 0, z' = z0
   zWquot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   zWquot(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   zWquot(z, z') -{ 0 }-> 1 + quot(z0, z2) + (1 + activate(z1) + activate(z3)) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0

Only complete derivations are relevant for the runtime complexity.

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

(155) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
We considered the (Usable) Rules:none
And the Tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(ACTIVATE(x_1)) = 0
   POL(MINUS(x_1, x_2)) = 0
   POL(QUOT(x_1, x_2)) = 0
   POL(SEL(x_1, x_2)) = [2]x_1
   POL(ZWQUOT(x_1, x_2)) = 0
   POL(activate(x_1)) = [3] + [2]x_1
   POL(c10(x_1)) = x_1
   POL(c11(x_1)) = x_1
   POL(c12(x_1)) = x_1
   POL(c15(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c5(x_1)) = x_1
   POL(c7(x_1, x_2)) = x_1 + x_2
   POL(cons(x_1, x_2)) = 0
   POL(from(x_1)) = [3] + [3]x_1
   POL(minus(x_1, x_2)) = [3]x_1 + [3]x_2
   POL(n__from(x_1)) = [3] + x_1
   POL(n__zWquot(x_1, x_2)) = 0
   POL(nil) = [3]
   POL(quot(x_1, x_2)) = [3] + [3]x_2
   POL(s(x_1)) = [1] + x_1
   POL(zWquot(x_1, x_2)) = [3]

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
K tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c5_1, c7_2, c10_1, c11_1, c12_1, c15_1


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

(157) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
We considered the (Usable) Rules:none
And the Tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(ACTIVATE(x_1)) = [1]
   POL(MINUS(x_1, x_2)) = 0
   POL(QUOT(x_1, x_2)) = 0
   POL(SEL(x_1, x_2)) = x_1
   POL(ZWQUOT(x_1, x_2)) = [1]
   POL(activate(x_1)) = [1] + x_1
   POL(c10(x_1)) = x_1
   POL(c11(x_1)) = x_1
   POL(c12(x_1)) = x_1
   POL(c15(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c5(x_1)) = x_1
   POL(c7(x_1, x_2)) = x_1 + x_2
   POL(cons(x_1, x_2)) = x_1
   POL(from(x_1)) = [1] + x_1
   POL(minus(x_1, x_2)) = [1] + x_1 + x_2
   POL(n__from(x_1)) = [1] + x_1
   POL(n__zWquot(x_1, x_2)) = [1] + x_1
   POL(nil) = [1]
   POL(quot(x_1, x_2)) = [1] + x_1 + x_2
   POL(s(x_1)) = [1] + x_1
   POL(zWquot(x_1, x_2)) = [1] + x_2

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
K tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c5_1, c7_2, c10_1, c11_1, c12_1, c15_1


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

(159) CdtRuleRemovalProof (UPPER BOUND(ADD(n^2)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
We considered the (Usable) Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   from(z0) -> n__from(z0)
   activate(n__from(z0)) -> from(z0)
   activate(z0) -> z0
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
And the Tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(ACTIVATE(x_1)) = [2]x_1
   POL(MINUS(x_1, x_2)) = 0
   POL(QUOT(x_1, x_2)) = 0
   POL(SEL(x_1, x_2)) = x_1*x_2
   POL(ZWQUOT(x_1, x_2)) = [2]x_1 + [2]x_2
   POL(activate(x_1)) = x_1
   POL(c10(x_1)) = x_1
   POL(c11(x_1)) = x_1
   POL(c12(x_1)) = x_1
   POL(c15(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c5(x_1)) = x_1
   POL(c7(x_1, x_2)) = x_1 + x_2
   POL(cons(x_1, x_2)) = x_2
   POL(from(x_1)) = 0
   POL(minus(x_1, x_2)) = [1]
   POL(n__from(x_1)) = 0
   POL(n__zWquot(x_1, x_2)) = [2] + x_1 + x_2
   POL(nil) = [2]
   POL(quot(x_1, x_2)) = [2]x_1 + [2]x_1*x_2 + [2]x_1^2
   POL(s(x_1)) = [2] + x_1
   POL(zWquot(x_1, x_2)) = [2] + x_1 + x_2

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
K tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c5_1, c7_2, c10_1, c11_1, c12_1, c15_1


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

(161) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
K tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c5_1, c7_2, c10_1, c11_1, c12_1, c15_1


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

(163) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2)) by 
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, from(z0)), ACTIVATE(n__from(z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(SEL(x0, zWquot(z0, z1)), ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, from(z0)), ACTIVATE(n__from(z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(SEL(x0, zWquot(z0, z1)), ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
K tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1, SEL_2

Compound Symbols:   c5_1, c7_2, c10_1, c11_1, c12_1, c15_1, c3_2


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

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(SEL(x0, zWquot(z0, z1)), ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, from(z0)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
K tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, QUOT_2, ZWQUOT_2, ACTIVATE_1, SEL_2

Compound Symbols:   c5_1, c7_2, c10_1, c11_1, c12_1, c15_1, c3_2, c3_1


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

(167) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace QUOT(s(z0), s(z1)) -> c7(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) by 
   QUOT(s(z0), s(0)) -> c7(QUOT(0, s(0)), MINUS(z0, 0))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(SEL(x0, zWquot(z0, z1)), ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, from(z0)))
   QUOT(s(z0), s(0)) -> c7(QUOT(0, s(0)), MINUS(z0, 0))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(z0), s(0)) -> c7(QUOT(0, s(0)), MINUS(z0, 0))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
K tuples:
   SEL(s(z0), cons(z1, z2)) -> c3(SEL(z0, activate(z2)), ACTIVATE(z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2


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

(169) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   QUOT(s(z0), s(0)) -> c7(QUOT(0, s(0)), MINUS(z0, 0))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(SEL(x0, zWquot(z0, z1)), ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, from(z0)))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2


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

(171) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(SEL(x0, zWquot(z0, z1)), ACTIVATE(n__zWquot(z0, z1))) by 
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(SEL(x0, nil), ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(SEL(x0, nil), ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(SEL(x0, n__zWquot(z0, z1)), ACTIVATE(n__zWquot(z0, z1)))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, from(z0)))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(SEL(x0, nil), ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(SEL(x0, nil), ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(SEL(x0, n__zWquot(z0, z1)), ACTIVATE(n__zWquot(z0, z1)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2


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

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, from(z0)))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2


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

(175) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, from(z0))) by 
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, n__from(z0)))

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, n__from(z0)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c7_2, c3_1


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

(177) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, n__from(z0)))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c7_2, c3_1


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

(179) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace QUOT(s(s(z0)), s(s(z1))) -> c7(QUOT(minus(z0, z1), s(s(z1))), MINUS(s(z0), s(z1))) by 
   QUOT(s(s(z0)), s(s(0))) -> c7(QUOT(0, s(s(0))), MINUS(s(z0), s(0)))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(z0)), s(s(0))) -> c7(QUOT(0, s(s(0))), MINUS(s(z0), s(0)))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(s(z0)), s(s(0))) -> c7(QUOT(0, s(s(0))), MINUS(s(z0), s(0)))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2, c7_1


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

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2, c7_1


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

(183) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2, c7_1


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

(185) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
We considered the (Usable) Rules:none
And the Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(ACTIVATE(x_1)) = [1]
   POL(MINUS(x_1, x_2)) = 0
   POL(QUOT(x_1, x_2)) = [1]
   POL(SEL(x_1, x_2)) = [1] + x_1
   POL(ZWQUOT(x_1, x_2)) = [1]
   POL(activate(x_1)) = [1] + x_1
   POL(c10(x_1)) = x_1
   POL(c11(x_1)) = x_1
   POL(c12(x_1)) = x_1
   POL(c15(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c7(x_1, x_2)) = x_1 + x_2
   POL(cons(x_1, x_2)) = 0
   POL(from(x_1)) = [1] + x_1
   POL(minus(x_1, x_2)) = [1] + x_1 + x_2
   POL(n__from(x_1)) = [1] + x_1
   POL(n__zWquot(x_1, x_2)) = [1]
   POL(nil) = [1]
   POL(quot(x_1, x_2)) = x_2
   POL(s(x_1)) = [1] + x_1
   POL(zWquot(x_1, x_2)) = [1] + x_1 + x_2

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))
S tuples:
   MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   MINUS_2, ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2

Compound Symbols:   c5_1, c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2, c7_1


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

(187) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MINUS(s(z0), s(z1)) -> c5(MINUS(z0, z1)) by 
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2, MINUS_2

Compound Symbols:   c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2, c7_1, c5_1


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

(189) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   QUOT(s(s(z0)), s(s(0))) -> c7(MINUS(s(z0), s(0)))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2, MINUS_2

Compound Symbols:   c10_1, c11_1, c12_1, c15_1, c3_2, c3_1, c7_2, c7_1, c5_1


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

(191) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c10(QUOT(z0, z2)) by 
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))

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

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2, MINUS_2

Compound Symbols:   c11_1, c12_1, c15_1, c3_2, c3_1, c7_2, c7_1, c5_1, c10_1


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

(193) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c11(ACTIVATE(z1)) by 
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))

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

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   ZWQUOT_2, ACTIVATE_1, SEL_2, QUOT_2, MINUS_2

Compound Symbols:   c12_1, c15_1, c3_2, c3_1, c7_2, c7_1, c5_1, c10_1, c11_1


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

(195) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ZWQUOT(cons(z0, z1), cons(z2, z3)) -> c12(ACTIVATE(z3)) by 
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))

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

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   ACTIVATE_1, SEL_2, QUOT_2, MINUS_2, ZWQUOT_2

Compound Symbols:   c15_1, c3_2, c3_1, c7_2, c7_1, c5_1, c10_1, c11_1, c12_1


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

(197) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__zWquot(z0, z1)) -> c15(ZWQUOT(z0, z1)) by 
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, QUOT_2, MINUS_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c3_1, c7_2, c7_1, c5_1, c10_1, c11_1, c12_1, c15_1


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

(199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   SEL(s(x0), cons(x1, n__zWquot(z0, nil))) -> c3(ACTIVATE(n__zWquot(z0, nil)))
   SEL(s(x0), cons(x1, n__zWquot(nil, z0))) -> c3(ACTIVATE(n__zWquot(nil, z0)))

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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0))
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, QUOT_2, MINUS_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c3_1, c7_2, c7_1, c5_1, c10_1, c11_1, c12_1, c15_1


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

(201) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(x0), cons(x1, z0)) -> c3(SEL(x0, z0), ACTIVATE(z0)) by 
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)), ACTIVATE(cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))), ACTIVATE(cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))), ACTIVATE(cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))), ACTIVATE(cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(SEL(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(SEL(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(SEL(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)), ACTIVATE(cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))), ACTIVATE(cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))), ACTIVATE(cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))), ACTIVATE(cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(SEL(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(SEL(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(SEL(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, QUOT_2, MINUS_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c3_1, c7_2, c7_1, c5_1, c10_1, c11_1, c12_1, c15_1


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

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1)))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, QUOT_2, MINUS_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c3_1, c7_2, c7_1, c5_1, c10_1, c11_1, c12_1, c15_1


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

(205) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(x0), cons(x1, n__zWquot(z0, z1))) -> c3(ACTIVATE(n__zWquot(z0, z1))) by 
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))

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

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0)))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, QUOT_2, MINUS_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c3_1, c7_2, c7_1, c5_1, c10_1, c11_1, c12_1, c15_1


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

(207) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(x0), cons(x1, n__from(z0))) -> c3(SEL(x0, cons(z0, n__from(s(z0))))) by 
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, QUOT_2, MINUS_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c7_2, c7_1, c5_1, c10_1, c11_1, c12_1, c15_1, c3_1


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

(209) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace QUOT(s(s(x0)), s(s(x1))) -> c7(MINUS(s(x0), s(x1))) by 
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))

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

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1)))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, QUOT_2, MINUS_2, ZWQUOT_2, ACTIVATE_1

Compound Symbols:   c3_2, c7_2, c5_1, c10_1, c11_1, c12_1, c15_1, c3_1, c7_1


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

(211) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MINUS(s(s(y0)), s(s(y1))) -> c5(MINUS(s(y0), s(y1))) by 
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
S tuples:
   QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, QUOT_2, ZWQUOT_2, ACTIVATE_1, MINUS_2

Compound Symbols:   c3_2, c7_2, c10_1, c11_1, c12_1, c15_1, c3_1, c7_1, c5_1


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

(213) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace QUOT(s(s(s(z0))), s(s(s(z1)))) -> c7(QUOT(minus(z0, z1), s(s(s(z1)))), MINUS(s(s(z0)), s(s(z1)))) by 
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(QUOT(minus(s(y0), s(y1)), s(s(s(s(y1))))), MINUS(s(s(s(y0))), s(s(s(y1)))))

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

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(QUOT(minus(s(y0), s(y1)), s(s(s(s(y1))))), MINUS(s(s(s(y0))), s(s(s(y1)))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(QUOT(minus(s(y0), s(y1)), s(s(s(s(y1))))), MINUS(s(s(s(y0))), s(s(s(y1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c11_1, c12_1, c15_1, c3_1, c7_1, c5_1, c7_2


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

(215) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ZWQUOT(cons(s(s(y0)), z1), cons(s(s(y1)), z3)) -> c10(QUOT(s(s(y0)), s(s(y1)))) by 
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))

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

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(QUOT(minus(s(y0), s(y1)), s(s(s(s(y1))))), MINUS(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(QUOT(minus(s(y0), s(y1)), s(s(s(s(y1))))), MINUS(s(s(s(y0))), s(s(s(y1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1)))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c11_1, c12_1, c15_1, c3_1, c7_1, c5_1, c7_2


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

(217) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ZWQUOT(cons(z0, n__zWquot(y0, y1)), cons(z2, z3)) -> c11(ACTIVATE(n__zWquot(y0, y1))) by 
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))

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

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(QUOT(minus(s(y0), s(y1)), s(s(s(s(y1))))), MINUS(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(QUOT(minus(s(y0), s(y1)), s(s(s(s(y1))))), MINUS(s(s(s(y0))), s(s(s(y1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c12_1, c15_1, c3_1, c7_1, c5_1, c7_2, c11_1


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

(219) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(QUOT(minus(s(y0), s(y1)), s(s(s(s(y1))))), MINUS(s(s(s(y0))), s(s(s(y1))))) by QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
----------------------------------------

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1)))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c12_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2


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

(221) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(y0, y1))) -> c12(ACTIVATE(n__zWquot(y0, y1))) by 
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))

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

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(223) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) -> c15(ZWQUOT(cons(s(s(y0)), y1), cons(s(s(y2)), y3))) by 
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), z3))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))

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

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(225) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) -> c15(ZWQUOT(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))) by 
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))

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

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(227) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) -> c15(ZWQUOT(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))) by 
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))

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

(228)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(229) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(s(y0)), cons(z1, cons(y1, y2))) -> c3(SEL(s(y0), cons(y1, y2))) by 
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))

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

(230)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(231) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(y2, y3)))) -> c3(SEL(s(y0), cons(y1, n__zWquot(y2, y3)))) by 
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))

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

(232)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(233) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(s(y0)), cons(z1, cons(y1, n__from(y2)))) -> c3(SEL(s(y0), cons(y1, n__from(y2)))) by 
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(z3)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(z3))))

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

(234)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(235) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) by 
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))

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

(236)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(237) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) by 
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(y5)), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(y5)), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(y5)), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(y5)), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(y6)), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(y6)), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(y6)), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(y6)), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))

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

(238)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(239) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) by 
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(y5)), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(y5)), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(y5)), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(y5)), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(y6)), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(y6)), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(y6)), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(y6)), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z4, n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z4, n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z4, n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z4, n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z4, n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z4, n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z4, n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z4, n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))

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

(240)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(241) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) by 
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))

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

(242)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(243) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(z0), cons(z1, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c3(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) by 
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(y5)), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(y5)), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(y5)), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(y5)), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(y6)), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(y6)), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(y6)), z6)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(y6)), z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(z3, z4)), cons(s(s(y2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))

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

(244)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(245) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(z0), cons(z1, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) by 
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(y5)), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(y5)), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(y5)), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(y5)), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(y6)), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(y6)), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(y6)), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(y6)), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(y0)), z3), cons(s(s(y2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z4, n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z4, n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z4, n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z4, n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z4, n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z4, n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z4, n__zWquot(z5, z6))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z4, n__zWquot(z5, z6)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(y1, y2)), cons(z4, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))

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

(246)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(247) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace SEL(s(s(y0)), cons(z1, n__from(z2))) -> c3(SEL(s(y0), cons(z2, n__from(s(z2))))) by 
   SEL(s(s(s(y0))), cons(z1, n__from(z2))) -> c3(SEL(s(s(y0)), cons(z2, n__from(s(z2)))))

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

(248)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(s(s(y0))), cons(z1, n__from(z2))) -> c3(SEL(s(s(y0)), cons(z2, n__from(s(z2)))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, QUOT_2, MINUS_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c7_1, c5_1, c11_1, c7_2, c12_1


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

(249) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace QUOT(s(s(s(y0))), s(s(s(y1)))) -> c7(MINUS(s(s(y0)), s(s(y1)))) by 
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(MINUS(s(s(s(y0))), s(s(s(y1)))))

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

(250)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(s(s(y0))), cons(z1, n__from(z2))) -> c3(SEL(s(s(y0)), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(MINUS(s(s(s(y0))), s(s(s(y1)))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(MINUS(s(s(s(y0))), s(s(s(y1)))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, MINUS_2, QUOT_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c5_1, c11_1, c7_2, c12_1, c7_1


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

(251) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1))))) by 
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))

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

(252)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__zWquot(z0, z1)) -> zWquot(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   zWquot(z0, nil) -> nil
   zWquot(nil, z0) -> nil
   zWquot(cons(z0, z1), cons(z2, z3)) -> cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))
   zWquot(z0, z1) -> n__zWquot(z0, z1)
   quot(0, s(z0)) -> 0
   quot(s(z0), s(z1)) -> s(quot(minus(z0, z1), s(z1)))
   minus(z0, 0) -> 0
   minus(s(z0), s(z1)) -> minus(z0, z1)
Tuples:
   SEL(s(x0), cons(x1, n__zWquot(cons(z0, z1), cons(z2, z3)))) -> c3(SEL(x0, cons(quot(z0, z2), n__zWquot(activate(z1), activate(z3)))), ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, z3))))
   ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y1))), z3)) -> c10(QUOT(s(s(s(y0))), s(s(s(y1)))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   SEL(s(s(y0)), cons(z1, cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5))))) -> c3(SEL(s(y0), cons(y1, n__zWquot(cons(y2, y3), cons(y4, y5)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, y3)))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, y3))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6)))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(cons(y3, y4), cons(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__zWquot(y3, y4))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__zWquot(y3, y4)))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, cons(y2, n__from(y3))))) -> c3(SEL(s(s(y0)), cons(z2, cons(y2, n__from(y3)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(s(y2))), y3), cons(s(s(s(y4))), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(s(s(y2)), y3), cons(s(s(y4)), y5)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, n__zWquot(y3, y4)), cons(y5, y6)))))
   SEL(s(s(z0)), cons(z1, cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6)))))) -> c3(SEL(s(z0), cons(z2, n__zWquot(cons(y2, y3), cons(y4, n__zWquot(y5, y6))))))
   SEL(s(s(s(y0))), cons(z1, cons(z2, n__from(y2)))) -> c3(SEL(s(s(y0)), cons(z2, n__from(y2))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), z3), cons(s(s(z4)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(y1, y2)), cons(s(s(s(y3))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5)))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(y1, y2)), cons(s(s(s(s(y3)))), z5))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(y1, y2)), cons(s(s(z4)), n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), z3), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z3), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z4)), n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(z2)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z4)), n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6)))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, z6))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(s(y4))), y5), cons(s(s(s(y6))), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(s(s(y4)), y5), cons(s(s(y6)), y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, n__zWquot(y5, y6)), cons(y7, y8))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(z3, z4)), cons(z5, n__zWquot(cons(y4, y5), cons(y6, n__zWquot(y7, y8)))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z3, z4)), cons(s(s(s(y2))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4))))) -> c3(ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z3, z4)), cons(s(s(s(s(y2)))), n__zWquot(y3, y4)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z5, n__zWquot(y6, y7)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8))))) -> c3(ACTIVATE(n__zWquot(cons(z2, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z5, n__zWquot(y7, y8)))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))))
   SEL(s(z0), cons(z1, n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))) -> c3(ACTIVATE(n__zWquot(cons(z2, z3), cons(z4, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))))
   SEL(s(s(s(y0))), cons(z1, n__from(z2))) -> c3(SEL(s(s(y0)), cons(z2, n__from(s(z2)))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(MINUS(s(s(s(y0))), s(s(s(y1)))))
S tuples:
   MINUS(s(s(s(y0))), s(s(s(y1)))) -> c5(MINUS(s(s(y0)), s(s(y1))))
   QUOT(s(s(s(s(z0)))), s(s(s(s(z1))))) -> c7(QUOT(minus(z0, z1), s(s(s(s(z1))))), MINUS(s(s(s(z0))), s(s(s(z1)))))
K tuples:
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))) -> c15(ZWQUOT(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))
   ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y1)))), z3)) -> c10(QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))), cons(z3, z4)) -> c11(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(s(y0))), y1), cons(s(s(s(y2))), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3)))) -> c12(ACTIVATE(n__zWquot(cons(s(s(y0)), y1), cons(s(s(y2)), y3))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4)))) -> c12(ACTIVATE(n__zWquot(cons(y0, n__zWquot(y1, y2)), cons(y3, y4))))
   ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4))))) -> c12(ACTIVATE(n__zWquot(cons(y0, y1), cons(y2, n__zWquot(y3, y4)))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3))) -> c15(ZWQUOT(cons(s(s(z0)), n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(s(s(z2)), z3)))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(s(s(z0)), z1), cons(s(s(z2)), n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4))) -> c15(ZWQUOT(cons(s(s(s(y0))), n__zWquot(z1, z2)), cons(s(s(s(y2))), z4)))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), n__zWquot(z1, z2)), cons(s(s(s(s(y2)))), z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z3, z4)))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, n__zWquot(z1, z2)), cons(z3, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   ACTIVATE(n__zWquot(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(y0))), z1), cons(s(s(s(y2))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(s(s(s(s(y0)))), z1), cons(s(s(s(s(y2)))), n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(s(y1))), y2), cons(s(s(s(y3))), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(s(s(y1)), y2), cons(s(s(y3)), y4))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, n__zWquot(y2, y3)), cons(y4, y5))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4)))) -> c15(ZWQUOT(cons(z0, n__zWquot(cons(y1, y2), cons(y3, n__zWquot(y4, y5)))), cons(z2, n__zWquot(z3, z4))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(s(y3))), y4), cons(s(s(s(y5))), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(s(s(y3)), y4), cons(s(s(y5)), y6)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, n__zWquot(y4, y5)), cons(y6, y7)))))
   ACTIVATE(n__zWquot(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7)))))) -> c15(ZWQUOT(cons(z0, z1), cons(z2, n__zWquot(cons(y3, y4), cons(y5, n__zWquot(y6, y7))))))
   QUOT(s(s(s(s(y0)))), s(s(s(s(y1))))) -> c7(MINUS(s(s(s(y0))), s(s(s(y1)))))
Defined Rule Symbols:   activate_1, from_1, zWquot_2, quot_2, minus_2

Defined Pair Symbols:   SEL_2, ZWQUOT_2, ACTIVATE_1, MINUS_2, QUOT_2

Compound Symbols:   c3_2, c10_1, c15_1, c3_1, c5_1, c11_1, c7_2, c12_1, c7_1