KILLED
proof of input_QQxqDe2JZM.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
        (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (14) CpxRNTS
        (15) InliningProof [UPPER BOUND(ID), 143 ms]
        (16) CpxRNTS
        (17) SimplificationProof [BOTH BOUNDS(ID, ID), 11 ms]
        (18) CpxRNTS
        (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 4 ms]
        (20) CpxRNTS
        (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (22) CpxRNTS
        (23) IntTrsBoundProof [UPPER BOUND(ID), 216 ms]
        (24) CpxRNTS
        (25) IntTrsBoundProof [UPPER BOUND(ID), 35 ms]
        (26) CpxRNTS
        (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) IntTrsBoundProof [UPPER BOUND(ID), 254 ms]
        (30) CpxRNTS
        (31) IntTrsBoundProof [UPPER BOUND(ID), 87 ms]
        (32) CpxRNTS
        (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
        (35) IntTrsBoundProof [UPPER BOUND(ID), 257 ms]
        (36) CpxRNTS
        (37) IntTrsBoundProof [UPPER BOUND(ID), 146 ms]
        (38) CpxRNTS
        (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (40) CpxRNTS
        (41) IntTrsBoundProof [UPPER BOUND(ID), 1370 ms]
        (42) CpxRNTS
        (43) IntTrsBoundProof [UPPER BOUND(ID), 38 ms]
        (44) CpxRNTS
        (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (46) CpxRNTS
        (47) IntTrsBoundProof [UPPER BOUND(ID), 1520 ms]
        (48) CpxRNTS
        (49) IntTrsBoundProof [UPPER BOUND(ID), 128 ms]
        (50) CpxRNTS
    (51) CompletionProof [UPPER BOUND(ID), 0 ms]
    (52) CpxTypedWeightedCompleteTrs
        (53) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (54) CpxRNTS
(55) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(56) CdtProblem
    (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 174 ms]
    (62) CdtProblem
    (63) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 42 ms]
    (64) CdtProblem
    (65) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 79 ms]
    (66) CdtProblem
    (67) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 23 ms]
    (92) CdtProblem
    (93) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2 ms]
    (112) CdtProblem
    (113) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtRewritingProof [BOTH BOUNDS(ID, ID), 1 ms]
    (128) CdtProblem
    (129) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 10 ms]
    (130) CdtProblem
    (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 4 ms]
    (132) CdtProblem
    (133) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 5 ms]
    (142) CdtProblem
    (143) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 29 ms]
    (146) CdtProblem
    (147) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 36 ms]
    (148) CdtProblem
    (149) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 13 ms]
    (150) CdtProblem
    (151) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 41 ms]
    (152) CdtProblem
    (153) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (154) CdtProblem
    (155) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CdtProblem
    (157) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) 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) RelTrsToWeightedTrsProof (UPPER BOUND(ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

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

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

(8)
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
----------------------------------------

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

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

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   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

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

(10)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

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

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

(12)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

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

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

   0 => 0
   nil => 0

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

(14)
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


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

(15) 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

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

(16)
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


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

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

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> 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


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

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

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

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

(20)
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}

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

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

(22)
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}

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

(23) 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

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

(24)
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]

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

(25) 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

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

(26)
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]

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

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

(28)
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]

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

(29) 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

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

(30)
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]

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

(31) 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'

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

(32)
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]

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

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

(34)
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]

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

(35) 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

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

(36)
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]

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

(37) 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'

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

(38)
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]

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

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

(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 + 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]

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

(41) 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

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

(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 + 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]

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

(43) 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

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

(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 + 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]

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

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

(46)
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]

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

(47) 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: ?

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

(48)
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

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

(49) 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: ?

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

(50)
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

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

(51) 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

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

(52)
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
----------------------------------------

(53) 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

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

(54)
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.

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

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

(56)
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


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

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

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

(58)
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


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

(59) 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))

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

(60)
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


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

(61) 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]

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

(62)
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


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

(63) 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

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

(64)
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


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

(65) 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

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

(66)
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


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

(67) 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))

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

(68)
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


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

(69) 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))

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

(70)
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


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

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

(72)
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


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

(73) 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)))

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

(74)
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


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

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

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

(76)
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


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

(77) 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)))

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

(78)
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


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

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

(80)
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


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

(81) 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)))

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

(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:
   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


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

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

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

(84)
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


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

(85) 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)))

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

(86)
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


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

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

(88)
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


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

(89) 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)))

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

(90)
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


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

(91) 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

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

(92)
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


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

(93) 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)))

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

(94)
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


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

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

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

(96)
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


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

(97) 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))))

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

(98)
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


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

(99) 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)))

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

(100)
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


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

(101) 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)))

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

(102)
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


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

(103) 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))))

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

(104)
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


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

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

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

(106)
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


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

(107) 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)))))

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

(108)
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


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

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

(110)
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


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

(111) 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)))))

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

(112)
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


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

(113) 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)))))

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

(114)
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


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

(115) 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))))

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

(116)
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


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

(117) 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))))

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

(118)
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


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

(119) 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)))))

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

(120)
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


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

(121) 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))))))

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

(122)
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


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

(123) 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)))))

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

(124)
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


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

(125) 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)))))

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

(126)
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))))
   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)))))
   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(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)))))
   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, c7_2, c11_1, c12_1


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

(127) 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)))))
----------------------------------------

(128)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(129) 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))))))

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

(130)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(131) 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))))))

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

(132)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(133) 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))))))

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

(134)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(135) 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))))

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

(136)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(137) 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))))))

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

(138)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(139) 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))))

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

(140)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(141) 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)))))

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

(142)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(143) 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)))))

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

(144)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(145) 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)))))))

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

(146)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(147) 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)))))

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

(148)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(149) 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)))))

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

(150)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(151) 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)))))))

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

(152)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(153) 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)))))

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

(154)
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)))))
   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)))))
   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)))))
   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, c12_1, c7_2


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

(155) 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)))))

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

(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(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)))))
   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)))))
   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)))))
   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, c12_1, c7_2, c7_1


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

(157) 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))))))

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

(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(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)))))
   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)))))
   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)))))
   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, c12_1, c7_2, c7_1