KILLED
proof of input_B4kFKB9xpA.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(6) CdtProblem
    (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxRelTRS
    (9) RenamingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (10) CpxRelTRS
        (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (12) typed CpxTrs
        (13) OrderProof [LOWER BOUND(ID), 0 ms]
        (14) typed CpxTrs
    (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 1 ms]
    (16) TRS for Loop Detection
(17) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) InliningProof [UPPER BOUND(ID), 141 ms]
        (30) CpxRNTS
        (31) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (32) CpxRNTS
    (33) CompletionProof [UPPER BOUND(ID), 0 ms]
    (34) CpxTypedWeightedCompleteTrs
        (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (36) CpxRNTS
(37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(38) CdtProblem
    (39) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (40) CdtProblem
    (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CpxRelTRS
        (49) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (50) CpxTRS
        (51) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CpxWeightedTrs
            (53) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
            (54) CpxWeightedTrs
            (55) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (56) CpxTypedWeightedTrs
            (57) CompletionProof [UPPER BOUND(ID), 0 ms]
            (58) CpxTypedWeightedCompleteTrs
                (59) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
                (60) CpxTypedWeightedCompleteTrs
                (61) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (62) CpxRNTS
                (63) InliningProof [UPPER BOUND(ID), 126 ms]
                (64) CpxRNTS
                (65) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
                (66) CpxRNTS
            (67) CompletionProof [UPPER BOUND(ID), 0 ms]
            (68) CpxTypedWeightedCompleteTrs
                (69) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (70) CpxRNTS
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
        (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (82) CdtProblem
        (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms]
        (88) CdtProblem
        (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms]
        (122) CdtProblem
        (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (130) CdtProblem
        (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (134) CdtProblem
        (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (136) CdtProblem
        (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (138) CdtProblem
        (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (140) CdtProblem
        (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (142) CdtProblem
        (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (144) CdtProblem
        (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (146) CdtProblem
        (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (148) CdtProblem
        (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (150) CdtProblem
        (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (152) CdtProblem
        (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (154) CdtProblem
        (155) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (156) CdtProblem
        (157) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (158) CdtProblem
        (159) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (160) CdtProblem
        (161) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (162) CdtProblem
        (163) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (164) CdtProblem
        (165) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (166) CdtProblem
        (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (168) CdtProblem
        (169) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (170) CdtProblem
        (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (174) CdtProblem
        (175) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (176) CdtProblem
        (177) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (178) CdtProblem
        (179) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (180) CdtProblem
        (181) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (182) CdtProblem
        (183) CdtRewritingProof [BOTH BOUNDS(ID, ID), 8 ms]
        (184) CdtProblem
        (185) CdtRewritingProof [BOTH BOUNDS(ID, ID), 6 ms]
        (186) CdtProblem
        (187) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (188) CdtProblem
        (189) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (190) CdtProblem
        (191) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (192) CdtProblem
        (193) CdtRewritingProof [BOTH BOUNDS(ID, ID), 12 ms]
        (194) CdtProblem
        (195) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (196) CdtProblem
        (197) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (198) CdtProblem
        (199) CdtRewritingProof [BOTH BOUNDS(ID, ID), 10 ms]
        (200) 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:

   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y)))
   adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y))))
   hd(cons(X, Y)) -> activate(X)
   tl(cons(X, Y)) -> activate(Y)
   0 -> n__0
   zeros -> n__zeros
   s(X) -> n__s(X)
   incr(X) -> n__incr(X)
   adx(X) -> n__adx(X)
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(X)) -> s(X)
   activate(n__incr(X)) -> incr(X)
   activate(n__adx(X)) -> adx(X)
   activate(X) -> X

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

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

(2)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y)))
   adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y))))
   hd(cons(X, Y)) -> activate(X)
   tl(cons(X, Y)) -> activate(Y)
   0' -> n__0
   zeros -> n__zeros
   s(X) -> n__s(X)
   incr(X) -> n__incr(X)
   adx(X) -> n__adx(X)
   activate(n__0) -> 0'
   activate(n__zeros) -> zeros
   activate(n__s(X)) -> s(X)
   activate(n__incr(X)) -> incr(X)
   activate(n__adx(X)) -> adx(X)
   activate(X) -> X

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

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

(4)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y)))
   adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y))))
   hd(cons(X, Y)) -> activate(X)
   tl(cons(X, Y)) -> activate(Y)
   0 -> n__0
   zeros -> n__zeros
   s(X) -> n__s(X)
   incr(X) -> n__incr(X)
   adx(X) -> n__adx(X)
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(X)) -> s(X)
   activate(n__incr(X)) -> incr(X)
   activate(n__adx(X)) -> adx(X)
   activate(X) -> X

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

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

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
   hd(cons(z0, z1)) -> activate(z0)
   tl(cons(z0, z1)) -> activate(z1)
   0 -> n__0
   s(z0) -> n__s(z0)
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
Tuples:
   NATS -> c(ADX(zeros), ZEROS)
   ZEROS -> c1
   ZEROS -> c2
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   INCR(z0) -> c5
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ADX(z0) -> c8
   HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
   TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
   0' -> c11
   S(z0) -> c12
   ACTIVATE(n__0) -> c13(0')
   ACTIVATE(n__zeros) -> c14(ZEROS)
   ACTIVATE(n__s(z0)) -> c15(S(z0))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ACTIVATE(z0) -> c18
S tuples:
   NATS -> c(ADX(zeros), ZEROS)
   ZEROS -> c1
   ZEROS -> c2
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   INCR(z0) -> c5
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ADX(z0) -> c8
   HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
   TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
   0' -> c11
   S(z0) -> c12
   ACTIVATE(n__0) -> c13(0')
   ACTIVATE(n__zeros) -> c14(ZEROS)
   ACTIVATE(n__s(z0)) -> c15(S(z0))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ACTIVATE(z0) -> c18
K tuples:none
Defined Rule Symbols:   nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1

Defined Pair Symbols:   NATS, ZEROS, INCR_1, ADX_1, HD_1, TL_1, 0', S_1, ACTIVATE_1

Compound Symbols:   c_2, c1, c2, c3_1, c4_1, c5, c6_2, c7_2, c8, c9_1, c10_1, c11, c12, c13_1, c14_1, c15_1, c16_1, c17_1, c18


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

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

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


The TRS R consists of the following rules:

   NATS -> c(ADX(zeros), ZEROS)
   ZEROS -> c1
   ZEROS -> c2
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   INCR(z0) -> c5
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ADX(z0) -> c8
   HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
   TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
   0' -> c11
   S(z0) -> c12
   ACTIVATE(n__0) -> c13(0')
   ACTIVATE(n__zeros) -> c14(ZEROS)
   ACTIVATE(n__s(z0)) -> c15(S(z0))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ACTIVATE(z0) -> c18

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

   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
   hd(cons(z0, z1)) -> activate(z0)
   tl(cons(z0, z1)) -> activate(z1)
   0 -> n__0
   s(z0) -> n__s(z0)
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0

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

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

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


The TRS R consists of the following rules:

   NATS -> c(ADX(zeros), ZEROS)
   ZEROS -> c1
   ZEROS -> c2
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   INCR(z0) -> c5
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ADX(z0) -> c8
   HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
   TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
   0' -> c11
   S(z0) -> c12
   ACTIVATE(n__0) -> c13(0')
   ACTIVATE(n__zeros) -> c14(ZEROS)
   ACTIVATE(n__s(z0)) -> c15(S(z0))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ACTIVATE(z0) -> c18

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

   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
   hd(cons(z0, z1)) -> activate(z0)
   tl(cons(z0, z1)) -> activate(z1)
   0' -> n__0
   s(z0) -> n__s(z0)
   activate(n__0) -> 0'
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0

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

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

(12)
Obligation:
Innermost TRS:
Rules:
NATS -> c(ADX(zeros), ZEROS)
ZEROS -> c1
ZEROS -> c2
INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
INCR(z0) -> c5
ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
ADX(z0) -> c8
HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
0' -> c11
S(z0) -> c12
ACTIVATE(n__0) -> c13(0')
ACTIVATE(n__zeros) -> c14(ZEROS)
ACTIVATE(n__s(z0)) -> c15(S(z0))
ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
ACTIVATE(z0) -> c18
nats -> adx(zeros)
zeros -> cons(n__0, n__zeros)
zeros -> n__zeros
incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
incr(z0) -> n__incr(z0)
adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
adx(z0) -> n__adx(z0)
hd(cons(z0, z1)) -> activate(z0)
tl(cons(z0, z1)) -> activate(z1)
0' -> n__0
s(z0) -> n__s(z0)
activate(n__0) -> 0'
activate(n__zeros) -> zeros
activate(n__s(z0)) -> s(z0)
activate(n__incr(z0)) -> incr(z0)
activate(n__adx(z0)) -> adx(z0)
activate(z0) -> z0

Types:
NATS :: c
c :: c6:c7:c8 -> c1:c2 -> c
ADX :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c6:c7:c8
zeros :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
ZEROS :: c1:c2
c1 :: c1:c2
c2 :: c1:c2
INCR :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c3:c4:c5
cons :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c3 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5
ACTIVATE :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c13:c14:c15:c16:c17:c18
c4 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5
c5 :: c3:c4:c5
c6 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8
activate :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
n__adx :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c7 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8
c8 :: c6:c7:c8
HD :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c9
c9 :: c13:c14:c15:c16:c17:c18 -> c9
TL :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c10
c10 :: c13:c14:c15:c16:c17:c18 -> c10
0' :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c11 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
S :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c12
c12 :: c12
n__0 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c13 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c13:c14:c15:c16:c17:c18
n__zeros :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c14 :: c1:c2 -> c13:c14:c15:c16:c17:c18
n__s :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c15 :: c12 -> c13:c14:c15:c16:c17:c18
n__incr :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c16 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18
c17 :: c6:c7:c8 -> c13:c14:c15:c16:c17:c18
c18 :: c13:c14:c15:c16:c17:c18
nats :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
adx :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
incr :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
hd :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
tl :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
s :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
hole_c1_19 :: c
hole_c6:c7:c82_19 :: c6:c7:c8
hole_c1:c23_19 :: c1:c2
hole_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr4_19 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
hole_c3:c4:c55_19 :: c3:c4:c5
hole_c13:c14:c15:c16:c17:c186_19 :: c13:c14:c15:c16:c17:c18
hole_c97_19 :: c9
hole_c108_19 :: c10
hole_c129_19 :: c12
gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19 :: Nat -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr

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

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
ADX, INCR, ACTIVATE, activate, adx, incr

They will be analysed ascendingly in the following order:
ADX = INCR
ADX = ACTIVATE
activate < ADX
INCR = ACTIVATE
activate = adx
activate = incr
adx = incr

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

(14)
Obligation:
Innermost TRS:
Rules:
NATS -> c(ADX(zeros), ZEROS)
ZEROS -> c1
ZEROS -> c2
INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
INCR(z0) -> c5
ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
ADX(z0) -> c8
HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
0' -> c11
S(z0) -> c12
ACTIVATE(n__0) -> c13(0')
ACTIVATE(n__zeros) -> c14(ZEROS)
ACTIVATE(n__s(z0)) -> c15(S(z0))
ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
ACTIVATE(z0) -> c18
nats -> adx(zeros)
zeros -> cons(n__0, n__zeros)
zeros -> n__zeros
incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
incr(z0) -> n__incr(z0)
adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
adx(z0) -> n__adx(z0)
hd(cons(z0, z1)) -> activate(z0)
tl(cons(z0, z1)) -> activate(z1)
0' -> n__0
s(z0) -> n__s(z0)
activate(n__0) -> 0'
activate(n__zeros) -> zeros
activate(n__s(z0)) -> s(z0)
activate(n__incr(z0)) -> incr(z0)
activate(n__adx(z0)) -> adx(z0)
activate(z0) -> z0

Types:
NATS :: c
c :: c6:c7:c8 -> c1:c2 -> c
ADX :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c6:c7:c8
zeros :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
ZEROS :: c1:c2
c1 :: c1:c2
c2 :: c1:c2
INCR :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c3:c4:c5
cons :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c3 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5
ACTIVATE :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c13:c14:c15:c16:c17:c18
c4 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5
c5 :: c3:c4:c5
c6 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8
activate :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
n__adx :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c7 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8
c8 :: c6:c7:c8
HD :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c9
c9 :: c13:c14:c15:c16:c17:c18 -> c9
TL :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c10
c10 :: c13:c14:c15:c16:c17:c18 -> c10
0' :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c11 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
S :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c12
c12 :: c12
n__0 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c13 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c13:c14:c15:c16:c17:c18
n__zeros :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c14 :: c1:c2 -> c13:c14:c15:c16:c17:c18
n__s :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c15 :: c12 -> c13:c14:c15:c16:c17:c18
n__incr :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
c16 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18
c17 :: c6:c7:c8 -> c13:c14:c15:c16:c17:c18
c18 :: c13:c14:c15:c16:c17:c18
nats :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
adx :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
incr :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
hd :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
tl :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
s :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
hole_c1_19 :: c
hole_c6:c7:c82_19 :: c6:c7:c8
hole_c1:c23_19 :: c1:c2
hole_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr4_19 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr
hole_c3:c4:c55_19 :: c3:c4:c5
hole_c13:c14:c15:c16:c17:c186_19 :: c13:c14:c15:c16:c17:c18
hole_c97_19 :: c9
hole_c108_19 :: c10
hole_c129_19 :: c12
gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19 :: Nat -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr


Generator Equations:
gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19(0) <=> n__0
gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19(+(x, 1)) <=> cons(n__0, gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19(x))


The following defined symbols remain to be analysed:
incr, ADX, INCR, ACTIVATE, activate, adx

They will be analysed ascendingly in the following order:
ADX = INCR
ADX = ACTIVATE
activate < ADX
INCR = ACTIVATE
activate = adx
activate = incr
adx = incr

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

(15) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

(16)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   NATS -> c(ADX(zeros), ZEROS)
   ZEROS -> c1
   ZEROS -> c2
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   INCR(z0) -> c5
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ADX(z0) -> c8
   HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
   TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
   0' -> c11
   S(z0) -> c12
   ACTIVATE(n__0) -> c13(0')
   ACTIVATE(n__zeros) -> c14(ZEROS)
   ACTIVATE(n__s(z0)) -> c15(S(z0))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ACTIVATE(z0) -> c18

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

   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
   hd(cons(z0, z1)) -> activate(z0)
   tl(cons(z0, z1)) -> activate(z1)
   0 -> n__0
   s(z0) -> n__s(z0)
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0

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

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

(18)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   nats -> adx(zeros) [1]
   zeros -> cons(n__0, n__zeros) [1]
   incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1]
   adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1]
   hd(cons(X, Y)) -> activate(X) [1]
   tl(cons(X, Y)) -> activate(Y) [1]
   0 -> n__0 [1]
   zeros -> n__zeros [1]
   s(X) -> n__s(X) [1]
   incr(X) -> n__incr(X) [1]
   adx(X) -> n__adx(X) [1]
   activate(n__0) -> 0 [1]
   activate(n__zeros) -> zeros [1]
   activate(n__s(X)) -> s(X) [1]
   activate(n__incr(X)) -> incr(X) [1]
   activate(n__adx(X)) -> adx(X) [1]
   activate(X) -> X [1]

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

(19) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
Renamed defined symbols to avoid conflicts with arithmetic symbols:

0 => 0'

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

(20)
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:

   nats -> adx(zeros) [1]
   zeros -> cons(n__0, n__zeros) [1]
   incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1]
   adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1]
   hd(cons(X, Y)) -> activate(X) [1]
   tl(cons(X, Y)) -> activate(Y) [1]
   0' -> n__0 [1]
   zeros -> n__zeros [1]
   s(X) -> n__s(X) [1]
   incr(X) -> n__incr(X) [1]
   adx(X) -> n__adx(X) [1]
   activate(n__0) -> 0' [1]
   activate(n__zeros) -> zeros [1]
   activate(n__s(X)) -> s(X) [1]
   activate(n__incr(X)) -> incr(X) [1]
   activate(n__adx(X)) -> adx(X) [1]
   activate(X) -> X [1]

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

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

(22)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   nats -> adx(zeros) [1]
   zeros -> cons(n__0, n__zeros) [1]
   incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1]
   adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1]
   hd(cons(X, Y)) -> activate(X) [1]
   tl(cons(X, Y)) -> activate(Y) [1]
   0' -> n__0 [1]
   zeros -> n__zeros [1]
   s(X) -> n__s(X) [1]
   incr(X) -> n__incr(X) [1]
   adx(X) -> n__adx(X) [1]
   activate(n__0) -> 0' [1]
   activate(n__zeros) -> zeros [1]
   activate(n__s(X)) -> s(X) [1]
   activate(n__incr(X)) -> incr(X) [1]
   activate(n__adx(X)) -> adx(X) [1]
   activate(X) -> X [1]

The TRS has the following type information:
nats :: n__0:n__zeros:cons:n__s:n__incr:n__adx
adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx
cons :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__0 :: n__0:n__zeros:cons:n__s:n__incr:n__adx
n__zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx
incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
activate :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
0' :: n__0:n__zeros:cons:n__s:n__incr:n__adx
s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx

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

(23) 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:

   nats
   hd_1
   tl_1

(c) The following functions are completely defined:

   zeros
   activate_1
   0'
   incr_1
   s_1
   adx_1

Due to the following rules being added:
none

And the following fresh constants: none

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

(24)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   nats -> adx(zeros) [1]
   zeros -> cons(n__0, n__zeros) [1]
   incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1]
   adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1]
   hd(cons(X, Y)) -> activate(X) [1]
   tl(cons(X, Y)) -> activate(Y) [1]
   0' -> n__0 [1]
   zeros -> n__zeros [1]
   s(X) -> n__s(X) [1]
   incr(X) -> n__incr(X) [1]
   adx(X) -> n__adx(X) [1]
   activate(n__0) -> 0' [1]
   activate(n__zeros) -> zeros [1]
   activate(n__s(X)) -> s(X) [1]
   activate(n__incr(X)) -> incr(X) [1]
   activate(n__adx(X)) -> adx(X) [1]
   activate(X) -> X [1]

The TRS has the following type information:
nats :: n__0:n__zeros:cons:n__s:n__incr:n__adx
adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx
cons :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__0 :: n__0:n__zeros:cons:n__s:n__incr:n__adx
n__zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx
incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
activate :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
0' :: n__0:n__zeros:cons:n__s:n__incr:n__adx
s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx

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

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

(26)
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:

   nats -> adx(cons(n__0, n__zeros)) [2]
   nats -> adx(n__zeros) [2]
   zeros -> cons(n__0, n__zeros) [1]
   incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1]
   adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1]
   hd(cons(X, Y)) -> activate(X) [1]
   tl(cons(X, Y)) -> activate(Y) [1]
   0' -> n__0 [1]
   zeros -> n__zeros [1]
   s(X) -> n__s(X) [1]
   incr(X) -> n__incr(X) [1]
   adx(X) -> n__adx(X) [1]
   activate(n__0) -> 0' [1]
   activate(n__zeros) -> zeros [1]
   activate(n__s(X)) -> s(X) [1]
   activate(n__incr(X)) -> incr(X) [1]
   activate(n__adx(X)) -> adx(X) [1]
   activate(X) -> X [1]

The TRS has the following type information:
nats :: n__0:n__zeros:cons:n__s:n__incr:n__adx
adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx
cons :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__0 :: n__0:n__zeros:cons:n__s:n__incr:n__adx
n__zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx
incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
activate :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
n__adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx
0' :: n__0:n__zeros:cons:n__s:n__incr:n__adx
s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx

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

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

   n__0 => 0
   n__zeros => 1

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

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   0' -{ 1 }-> 0 :|: 
   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> zeros :|: z = 1
   activate(z) -{ 1 }-> s(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> incr(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> adx(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> 0' :|: z = 0
   adx(z) -{ 1 }-> incr(1 + activate(X) + (1 + activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0
   adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   hd(z) -{ 1 }-> activate(X) :|: Y >= 0, z = 1 + X + Y, X >= 0
   incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   incr(z) -{ 1 }-> 1 + (1 + activate(X)) + (1 + activate(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   nats -{ 2 }-> adx(1) :|: 
   nats -{ 2 }-> adx(1 + 0 + 1) :|: 
   s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   tl(z) -{ 1 }-> activate(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   zeros -{ 1 }-> 1 :|: 
   zeros -{ 1 }-> 1 + 0 + 1 :|: 


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

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

   zeros -{ 1 }-> 1 :|: 
   zeros -{ 1 }-> 1 + 0 + 1 :|: 
   0' -{ 1 }-> 0 :|: 
   s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X

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

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   0' -{ 1 }-> 0 :|: 
   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> incr(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> adx(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z = 1 + X, X >= 0, X' >= 0, X = X'
   activate(z) -{ 2 }-> 1 + 0 + 1 :|: z = 1
   adx(z) -{ 1 }-> incr(1 + activate(X) + (1 + activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0
   adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   hd(z) -{ 1 }-> activate(X) :|: Y >= 0, z = 1 + X + Y, X >= 0
   incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   incr(z) -{ 1 }-> 1 + (1 + activate(X)) + (1 + activate(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   nats -{ 2 }-> adx(1) :|: 
   nats -{ 2 }-> adx(1 + 0 + 1) :|: 
   s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   tl(z) -{ 1 }-> activate(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   zeros -{ 1 }-> 1 :|: 
   zeros -{ 1 }-> 1 + 0 + 1 :|: 


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

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

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   0' -{ 1 }-> 0 :|: 
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 1 }-> incr(z - 1) :|: z - 1 >= 0
   activate(z) -{ 1 }-> adx(z - 1) :|: z - 1 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + 0 + 1 :|: z = 1
   adx(z) -{ 1 }-> incr(1 + activate(X) + (1 + activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0
   adx(z) -{ 1 }-> 1 + z :|: z >= 0
   hd(z) -{ 1 }-> activate(X) :|: Y >= 0, z = 1 + X + Y, X >= 0
   incr(z) -{ 1 }-> 1 + z :|: z >= 0
   incr(z) -{ 1 }-> 1 + (1 + activate(X)) + (1 + activate(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   nats -{ 2 }-> adx(1) :|: 
   nats -{ 2 }-> adx(1 + 0 + 1) :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0
   tl(z) -{ 1 }-> activate(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   zeros -{ 1 }-> 1 :|: 
   zeros -{ 1 }-> 1 + 0 + 1 :|: 


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

(33) 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:

   hd(v0) -> null_hd [0]
   tl(v0) -> null_tl [0]

And the following fresh constants:    null_hd, null_tl

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

(34)
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:

   nats -> adx(zeros) [1]
   zeros -> cons(n__0, n__zeros) [1]
   incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1]
   adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1]
   hd(cons(X, Y)) -> activate(X) [1]
   tl(cons(X, Y)) -> activate(Y) [1]
   0' -> n__0 [1]
   zeros -> n__zeros [1]
   s(X) -> n__s(X) [1]
   incr(X) -> n__incr(X) [1]
   adx(X) -> n__adx(X) [1]
   activate(n__0) -> 0' [1]
   activate(n__zeros) -> zeros [1]
   activate(n__s(X)) -> s(X) [1]
   activate(n__incr(X)) -> incr(X) [1]
   activate(n__adx(X)) -> adx(X) [1]
   activate(X) -> X [1]
   hd(v0) -> null_hd [0]
   tl(v0) -> null_tl [0]

The TRS has the following type information:
nats :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
cons :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
n__0 :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
n__zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
n__s :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
activate :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
n__incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
n__adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
0' :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
s :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
null_hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl
null_tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl

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

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

   n__0 => 0
   n__zeros => 1
   null_hd => 0
   null_tl => 0

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

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

   0' -{ 1 }-> 0 :|: 
   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> zeros :|: z = 1
   activate(z) -{ 1 }-> s(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> incr(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> adx(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> 0' :|: z = 0
   adx(z) -{ 1 }-> incr(1 + activate(X) + (1 + activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0
   adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   hd(z) -{ 1 }-> activate(X) :|: Y >= 0, z = 1 + X + Y, X >= 0
   hd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   incr(z) -{ 1 }-> 1 + (1 + activate(X)) + (1 + activate(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   nats -{ 1 }-> adx(zeros) :|: 
   s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   tl(z) -{ 1 }-> activate(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   tl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   zeros -{ 1 }-> 1 :|: 
   zeros -{ 1 }-> 1 + 0 + 1 :|: 

Only complete derivations are relevant for the runtime complexity.

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

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
   hd(cons(z0, z1)) -> activate(z0)
   tl(cons(z0, z1)) -> activate(z1)
   0 -> n__0
   s(z0) -> n__s(z0)
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
Tuples:
   NATS -> c(ADX(zeros), ZEROS)
   ZEROS -> c1
   ZEROS -> c2
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   INCR(z0) -> c5
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ADX(z0) -> c8
   HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
   TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
   0' -> c11
   S(z0) -> c12
   ACTIVATE(n__0) -> c13(0')
   ACTIVATE(n__zeros) -> c14(ZEROS)
   ACTIVATE(n__s(z0)) -> c15(S(z0))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ACTIVATE(z0) -> c18
S tuples:
   NATS -> c(ADX(zeros), ZEROS)
   ZEROS -> c1
   ZEROS -> c2
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   INCR(z0) -> c5
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ADX(z0) -> c8
   HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
   TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
   0' -> c11
   S(z0) -> c12
   ACTIVATE(n__0) -> c13(0')
   ACTIVATE(n__zeros) -> c14(ZEROS)
   ACTIVATE(n__s(z0)) -> c15(S(z0))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ACTIVATE(z0) -> c18
K tuples:none
Defined Rule Symbols:   nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1

Defined Pair Symbols:   NATS, ZEROS, INCR_1, ADX_1, HD_1, TL_1, 0', S_1, ACTIVATE_1

Compound Symbols:   c_2, c1, c2, c3_1, c4_1, c5, c6_2, c7_2, c8, c9_1, c10_1, c11, c12, c13_1, c14_1, c15_1, c16_1, c17_1, c18


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

(39) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   HD(cons(z0, z1)) -> c9(ACTIVATE(z0))
   TL(cons(z0, z1)) -> c10(ACTIVATE(z1))
Removed 10 trailing nodes:
   ACTIVATE(z0) -> c18
   0' -> c11
   ACTIVATE(n__zeros) -> c14(ZEROS)
   ACTIVATE(n__s(z0)) -> c15(S(z0))
   ZEROS -> c2
   ACTIVATE(n__0) -> c13(0')
   INCR(z0) -> c5
   S(z0) -> c12
   ADX(z0) -> c8
   ZEROS -> c1

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
   hd(cons(z0, z1)) -> activate(z0)
   tl(cons(z0, z1)) -> activate(z1)
   0 -> n__0
   s(z0) -> n__s(z0)
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
Tuples:
   NATS -> c(ADX(zeros), ZEROS)
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
S tuples:
   NATS -> c(ADX(zeros), ZEROS)
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
K tuples:none
Defined Rule Symbols:   nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1

Defined Pair Symbols:   NATS, INCR_1, ADX_1, ACTIVATE_1

Compound Symbols:   c_2, c3_1, c4_1, c6_2, c7_2, c16_1, c17_1


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
   hd(cons(z0, z1)) -> activate(z0)
   tl(cons(z0, z1)) -> activate(z1)
   0 -> n__0
   s(z0) -> n__s(z0)
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   NATS -> c(ADX(zeros))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   NATS -> c(ADX(zeros))
K tuples:none
Defined Rule Symbols:   nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1

Defined Pair Symbols:   INCR_1, ADX_1, ACTIVATE_1, NATS

Compound Symbols:   c3_1, c4_1, c6_2, c7_2, c16_1, c17_1, c_1


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

(43) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   NATS -> c(ADX(zeros))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   nats -> adx(zeros)
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
   hd(cons(z0, z1)) -> activate(z0)
   tl(cons(z0, z1)) -> activate(z1)
   0 -> n__0
   s(z0) -> n__s(z0)
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   NATS -> c(ADX(zeros))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
K tuples:
   NATS -> c(ADX(zeros))
Defined Rule Symbols:   nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1

Defined Pair Symbols:   INCR_1, ADX_1, ACTIVATE_1, NATS

Compound Symbols:   c3_1, c4_1, c6_2, c7_2, c16_1, c17_1, c_1


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

(45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   nats -> adx(zeros)
   hd(cons(z0, z1)) -> activate(z0)
   tl(cons(z0, z1)) -> activate(z1)

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   NATS -> c(ADX(zeros))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
K tuples:
   NATS -> c(ADX(zeros))
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ADX_1, ACTIVATE_1, NATS

Compound Symbols:   c3_1, c4_1, c6_2, c7_2, c16_1, c17_1, c_1


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

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

(48)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))

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

   NATS -> c(ADX(zeros))
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)

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

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

(50)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   NATS -> c(ADX(zeros))
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)

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

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

(52)
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:

   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1]
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1]
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1]
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1]
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1]
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1]
   NATS -> c(ADX(zeros)) [0]
   activate(n__0) -> 0 [0]
   activate(n__zeros) -> zeros [0]
   activate(n__s(z0)) -> s(z0) [0]
   activate(n__incr(z0)) -> incr(z0) [0]
   activate(n__adx(z0)) -> adx(z0) [0]
   activate(z0) -> z0 [0]
   0 -> n__0 [0]
   zeros -> cons(n__0, n__zeros) [0]
   zeros -> n__zeros [0]
   s(z0) -> n__s(z0) [0]
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0]
   incr(z0) -> n__incr(z0) [0]
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0]
   adx(z0) -> n__adx(z0) [0]

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

(53) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
Renamed defined symbols to avoid conflicts with arithmetic symbols:

0 => 0'

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

(54)
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:

   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1]
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1]
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1]
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1]
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1]
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1]
   NATS -> c(ADX(zeros)) [0]
   activate(n__0) -> 0' [0]
   activate(n__zeros) -> zeros [0]
   activate(n__s(z0)) -> s(z0) [0]
   activate(n__incr(z0)) -> incr(z0) [0]
   activate(n__adx(z0)) -> adx(z0) [0]
   activate(z0) -> z0 [0]
   0' -> n__0 [0]
   zeros -> cons(n__0, n__zeros) [0]
   zeros -> n__zeros [0]
   s(z0) -> n__s(z0) [0]
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0]
   incr(z0) -> n__incr(z0) [0]
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0]
   adx(z0) -> n__adx(z0) [0]

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

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

(56)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1]
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1]
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1]
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1]
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1]
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1]
   NATS -> c(ADX(zeros)) [0]
   activate(n__0) -> 0' [0]
   activate(n__zeros) -> zeros [0]
   activate(n__s(z0)) -> s(z0) [0]
   activate(n__incr(z0)) -> incr(z0) [0]
   activate(n__adx(z0)) -> adx(z0) [0]
   activate(z0) -> z0 [0]
   0' -> n__0 [0]
   zeros -> cons(n__0, n__zeros) [0]
   zeros -> n__zeros [0]
   s(z0) -> n__s(z0) [0]
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0]
   incr(z0) -> n__incr(z0) [0]
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0]
   adx(z0) -> n__adx(z0) [0]

The TRS has the following type information:
INCR :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> c3:c4
cons :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s
c3 :: c16:c17 -> c3:c4
ACTIVATE :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> c16:c17
c4 :: c16:c17 -> c3:c4
ADX :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> c6:c7
c6 :: c3:c4 -> c16:c17 -> c6:c7
activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s
n__adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s
c7 :: c3:c4 -> c16:c17 -> c6:c7
n__incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s
c16 :: c3:c4 -> c16:c17
c17 :: c6:c7 -> c16:c17
NATS :: c
c :: c6:c7 -> c
zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s
n__0 :: cons:n__adx:n__incr:n__0:n__zeros:n__s
0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s
n__zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s
n__s :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s
s :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s
incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s
adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s

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

(57) 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:

   INCR_1
   ADX_1
   ACTIVATE_1

(c) The following functions are completely defined:

   NATS
   activate_1
   0'
   zeros
   s_1
   incr_1
   adx_1

Due to the following rules being added:

   NATS -> const3 [0]
   activate(v0) -> null_activate [0]
   0' -> null_0' [0]
   zeros -> null_zeros [0]
   s(v0) -> null_s [0]
   incr(v0) -> null_incr [0]
   adx(v0) -> null_adx [0]

And the following fresh constants:    const3, null_activate, null_0', null_zeros, null_s, null_incr, null_adx, const, const1, const2

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

(58)
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:

   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1]
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1]
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1]
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1]
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1]
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1]
   NATS -> c(ADX(zeros)) [0]
   activate(n__0) -> 0' [0]
   activate(n__zeros) -> zeros [0]
   activate(n__s(z0)) -> s(z0) [0]
   activate(n__incr(z0)) -> incr(z0) [0]
   activate(n__adx(z0)) -> adx(z0) [0]
   activate(z0) -> z0 [0]
   0' -> n__0 [0]
   zeros -> cons(n__0, n__zeros) [0]
   zeros -> n__zeros [0]
   s(z0) -> n__s(z0) [0]
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0]
   incr(z0) -> n__incr(z0) [0]
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0]
   adx(z0) -> n__adx(z0) [0]
   NATS -> const3 [0]
   activate(v0) -> null_activate [0]
   0' -> null_0' [0]
   zeros -> null_zeros [0]
   s(v0) -> null_s [0]
   incr(v0) -> null_incr [0]
   adx(v0) -> null_adx [0]

The TRS has the following type information:
INCR :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c3:c4
cons :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
c3 :: c16:c17 -> c3:c4
ACTIVATE :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c16:c17
c4 :: c16:c17 -> c3:c4
ADX :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c6:c7
c6 :: c3:c4 -> c16:c17 -> c6:c7
activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
c7 :: c3:c4 -> c16:c17 -> c6:c7
n__incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
c16 :: c3:c4 -> c16:c17
c17 :: c6:c7 -> c16:c17
NATS :: c:const3
c :: c6:c7 -> c:const3
zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__0 :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
const3 :: c:const3
null_activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
const :: c3:c4
const1 :: c16:c17
const2 :: c6:c7

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

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

(60)
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:

   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1]
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1]
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1]
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1]
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1]
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1]
   NATS -> c(ADX(cons(n__0, n__zeros))) [0]
   NATS -> c(ADX(n__zeros)) [0]
   NATS -> c(ADX(null_zeros)) [0]
   activate(n__0) -> 0' [0]
   activate(n__zeros) -> zeros [0]
   activate(n__s(z0)) -> s(z0) [0]
   activate(n__incr(z0)) -> incr(z0) [0]
   activate(n__adx(z0)) -> adx(z0) [0]
   activate(z0) -> z0 [0]
   0' -> n__0 [0]
   zeros -> cons(n__0, n__zeros) [0]
   zeros -> n__zeros [0]
   s(z0) -> n__s(z0) [0]
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0]
   incr(z0) -> n__incr(z0) [0]
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0]
   adx(z0) -> n__adx(z0) [0]
   NATS -> const3 [0]
   activate(v0) -> null_activate [0]
   0' -> null_0' [0]
   zeros -> null_zeros [0]
   s(v0) -> null_s [0]
   incr(v0) -> null_incr [0]
   adx(v0) -> null_adx [0]

The TRS has the following type information:
INCR :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c3:c4
cons :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
c3 :: c16:c17 -> c3:c4
ACTIVATE :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c16:c17
c4 :: c16:c17 -> c3:c4
ADX :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c6:c7
c6 :: c3:c4 -> c16:c17 -> c6:c7
activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
c7 :: c3:c4 -> c16:c17 -> c6:c7
n__incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
c16 :: c3:c4 -> c16:c17
c17 :: c6:c7 -> c16:c17
NATS :: c:const3
c :: c6:c7 -> c:const3
zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__0 :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
const3 :: c:const3
null_activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
const :: c3:c4
const1 :: c16:c17
const2 :: c6:c7

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

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

   n__0 => 0
   n__zeros => 1
   const3 => 0
   null_activate => 0
   null_0' => 0
   null_zeros => 0
   null_s => 0
   null_incr => 0
   null_adx => 0
   const => 0
   const1 => 0
   const2 => 0

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

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

   0' -{ 0 }-> 0 :|: 
   ACTIVATE(z) -{ 1 }-> 1 + INCR(z0) :|: z = 1 + z0, z0 >= 0
   ACTIVATE(z) -{ 1 }-> 1 + ADX(z0) :|: z = 1 + z0, z0 >= 0
   ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INCR(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INCR(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   NATS -{ 0 }-> 0 :|: 
   NATS -{ 0 }-> 1 + ADX(1) :|: 
   NATS -{ 0 }-> 1 + ADX(0) :|: 
   NATS -{ 0 }-> 1 + ADX(1 + 0 + 1) :|: 
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> zeros :|: z = 1
   activate(z) -{ 0 }-> s(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> incr(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> adx(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> 0' :|: z = 0
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   adx(z) -{ 0 }-> incr(1 + activate(z0) + (1 + activate(z1))) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   incr(z) -{ 0 }-> 1 + (1 + activate(z0)) + (1 + activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   zeros -{ 0 }-> 1 :|: 
   zeros -{ 0 }-> 0 :|: 
   zeros -{ 0 }-> 1 + 0 + 1 :|: 


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

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

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

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

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

   0' -{ 0 }-> 0 :|: 
   ACTIVATE(z) -{ 1 }-> 1 + INCR(z0) :|: z = 1 + z0, z0 >= 0
   ACTIVATE(z) -{ 1 }-> 1 + ADX(z0) :|: z = 1 + z0, z0 >= 0
   ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INCR(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INCR(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   NATS -{ 0 }-> 0 :|: 
   NATS -{ 0 }-> 1 + ADX(1) :|: 
   NATS -{ 0 }-> 1 + ADX(0) :|: 
   NATS -{ 0 }-> 1 + ADX(1 + 0 + 1) :|: 
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> incr(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> adx(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> 1 :|: z = 1
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z = 1
   activate(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, z0 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, z0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + 0 + 1 :|: z = 1
   adx(z) -{ 0 }-> incr(1 + activate(z0) + (1 + activate(z1))) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   incr(z) -{ 0 }-> 1 + (1 + activate(z0)) + (1 + activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   zeros -{ 0 }-> 1 :|: 
   zeros -{ 0 }-> 0 :|: 
   zeros -{ 0 }-> 1 + 0 + 1 :|: 


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

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

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

   0' -{ 0 }-> 0 :|: 
   ACTIVATE(z) -{ 1 }-> 1 + INCR(z - 1) :|: z - 1 >= 0
   ACTIVATE(z) -{ 1 }-> 1 + ADX(z - 1) :|: z - 1 >= 0
   ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INCR(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INCR(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   NATS -{ 0 }-> 0 :|: 
   NATS -{ 0 }-> 1 + ADX(1) :|: 
   NATS -{ 0 }-> 1 + ADX(0) :|: 
   NATS -{ 0 }-> 1 + ADX(1 + 0 + 1) :|: 
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> incr(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> adx(z - 1) :|: z - 1 >= 0
   activate(z) -{ 0 }-> 1 :|: z = 1
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z = 1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + 0 + 1 :|: z = 1
   adx(z) -{ 0 }-> incr(1 + activate(z0) + (1 + activate(z1))) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   adx(z) -{ 0 }-> 0 :|: z >= 0
   adx(z) -{ 0 }-> 1 + z :|: z >= 0
   incr(z) -{ 0 }-> 0 :|: z >= 0
   incr(z) -{ 0 }-> 1 + z :|: z >= 0
   incr(z) -{ 0 }-> 1 + (1 + activate(z0)) + (1 + activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0
   zeros -{ 0 }-> 1 :|: 
   zeros -{ 0 }-> 0 :|: 
   zeros -{ 0 }-> 1 + 0 + 1 :|: 


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

(67) 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:

   NATS -> null_NATS [0]
   activate(v0) -> null_activate [0]
   0' -> null_0' [0]
   zeros -> null_zeros [0]
   s(v0) -> null_s [0]
   incr(v0) -> null_incr [0]
   adx(v0) -> null_adx [0]
   INCR(v0) -> null_INCR [0]
   ADX(v0) -> null_ADX [0]
   ACTIVATE(v0) -> null_ACTIVATE [0]

And the following fresh constants:    null_NATS, null_activate, null_0', null_zeros, null_s, null_incr, null_adx, null_INCR, null_ADX, null_ACTIVATE

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

(68)
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:

   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1]
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1]
   ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1]
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1]
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1]
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1]
   NATS -> c(ADX(zeros)) [0]
   activate(n__0) -> 0' [0]
   activate(n__zeros) -> zeros [0]
   activate(n__s(z0)) -> s(z0) [0]
   activate(n__incr(z0)) -> incr(z0) [0]
   activate(n__adx(z0)) -> adx(z0) [0]
   activate(z0) -> z0 [0]
   0' -> n__0 [0]
   zeros -> cons(n__0, n__zeros) [0]
   zeros -> n__zeros [0]
   s(z0) -> n__s(z0) [0]
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0]
   incr(z0) -> n__incr(z0) [0]
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0]
   adx(z0) -> n__adx(z0) [0]
   NATS -> null_NATS [0]
   activate(v0) -> null_activate [0]
   0' -> null_0' [0]
   zeros -> null_zeros [0]
   s(v0) -> null_s [0]
   incr(v0) -> null_incr [0]
   adx(v0) -> null_adx [0]
   INCR(v0) -> null_INCR [0]
   ADX(v0) -> null_ADX [0]
   ACTIVATE(v0) -> null_ACTIVATE [0]

The TRS has the following type information:
INCR :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c3:c4:null_INCR
cons :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
c3 :: c16:c17:null_ACTIVATE -> c3:c4:null_INCR
ACTIVATE :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c16:c17:null_ACTIVATE
c4 :: c16:c17:null_ACTIVATE -> c3:c4:null_INCR
ADX :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c6:c7:null_ADX
c6 :: c3:c4:null_INCR -> c16:c17:null_ACTIVATE -> c6:c7:null_ADX
activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
c7 :: c3:c4:null_INCR -> c16:c17:null_ACTIVATE -> c6:c7:null_ADX
n__incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
c16 :: c3:c4:null_INCR -> c16:c17:null_ACTIVATE
c17 :: c6:c7:null_ADX -> c16:c17:null_ACTIVATE
NATS :: c:null_NATS
c :: c6:c7:null_ADX -> c:null_NATS
zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__0 :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
n__s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_NATS :: c:null_NATS
null_activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx
null_INCR :: c3:c4:null_INCR
null_ADX :: c6:c7:null_ADX
null_ACTIVATE :: c16:c17:null_ACTIVATE

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

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

   n__0 => 0
   n__zeros => 1
   null_NATS => 0
   null_activate => 0
   null_0' => 0
   null_zeros => 0
   null_s => 0
   null_incr => 0
   null_adx => 0
   null_INCR => 0
   null_ADX => 0
   null_ACTIVATE => 0

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

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

   0' -{ 0 }-> 0 :|: 
   ACTIVATE(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   ACTIVATE(z) -{ 1 }-> 1 + INCR(z0) :|: z = 1 + z0, z0 >= 0
   ACTIVATE(z) -{ 1 }-> 1 + ADX(z0) :|: z = 1 + z0, z0 >= 0
   ADX(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INCR(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   INCR(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INCR(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   NATS -{ 0 }-> 0 :|: 
   NATS -{ 0 }-> 1 + ADX(zeros) :|: 
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> zeros :|: z = 1
   activate(z) -{ 0 }-> s(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> incr(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> adx(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> 0' :|: z = 0
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   adx(z) -{ 0 }-> incr(1 + activate(z0) + (1 + activate(z1))) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   incr(z) -{ 0 }-> 1 + (1 + activate(z0)) + (1 + activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   zeros -{ 0 }-> 1 :|: 
   zeros -{ 0 }-> 0 :|: 
   zeros -{ 0 }-> 1 + 0 + 1 :|: 

Only complete derivations are relevant for the runtime complexity.

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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) by 
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   NATS -> c(ADX(zeros))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
K tuples:
   NATS -> c(ADX(zeros))
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ADX_1, ACTIVATE_1, NATS

Compound Symbols:   c3_1, c4_1, c7_2, c16_1, c17_1, c_1, c6_2


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   NATS -> c(ADX(zeros))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
K tuples:
   NATS -> c(ADX(zeros))
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ADX_1, ACTIVATE_1, NATS

Compound Symbols:   c3_1, c4_1, c7_2, c16_1, c17_1, c_1, c6_2, c6_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) by 
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   NATS -> c(ADX(zeros))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
K tuples:
   NATS -> c(ADX(zeros))
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, NATS, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c_1, c6_2, c6_1, c7_2


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

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   NATS -> c(ADX(zeros))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
K tuples:
   NATS -> c(ADX(zeros))
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, NATS, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c_1, c6_2, c6_1, c7_2, c7_1


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace NATS -> c(ADX(zeros)) by 
   NATS -> c(ADX(cons(n__0, n__zeros)))
   NATS -> c(ADX(n__zeros))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   NATS -> c(ADX(cons(n__0, n__zeros)))
   NATS -> c(ADX(n__zeros))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
K tuples:
   NATS -> c(ADX(zeros))
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1, NATS

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1, c_1


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

(81) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   NATS -> c(ADX(cons(n__0, n__zeros)))
Removed 1 trailing nodes:
   NATS -> c(ADX(n__zeros))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) by 
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) by 
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) by 
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) by 
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) by 
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) by 
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))), ACTIVATE(n__0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))), ACTIVATE(n__0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))), ACTIVATE(n__0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))), ACTIVATE(n__zeros))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) by 
   ADX(cons(n__incr(x0), n__0)) -> c6(INCR(cons(incr(x0), n__adx(0))), ACTIVATE(n__incr(x0)))
   ADX(cons(n__incr(x0), n__zeros)) -> c6(INCR(cons(incr(x0), n__adx(zeros))), ACTIVATE(n__incr(x0)))
   ADX(cons(n__incr(x0), n__s(z0))) -> c6(INCR(cons(incr(x0), n__adx(s(z0)))), ACTIVATE(n__incr(x0)))
   ADX(cons(n__incr(x0), n__incr(z0))) -> c6(INCR(cons(incr(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(x0)))
   ADX(cons(n__incr(x0), n__adx(z0))) -> c6(INCR(cons(incr(x0), n__adx(adx(z0)))), ACTIVATE(n__incr(x0)))
   ADX(cons(n__incr(x0), z0)) -> c6(INCR(cons(incr(x0), n__adx(z0))), ACTIVATE(n__incr(x0)))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) by 
   ADX(cons(n__adx(x0), n__0)) -> c6(INCR(cons(adx(x0), n__adx(0))), ACTIVATE(n__adx(x0)))
   ADX(cons(n__adx(x0), n__zeros)) -> c6(INCR(cons(adx(x0), n__adx(zeros))), ACTIVATE(n__adx(x0)))
   ADX(cons(n__adx(x0), n__s(z0))) -> c6(INCR(cons(adx(x0), n__adx(s(z0)))), ACTIVATE(n__adx(x0)))
   ADX(cons(n__adx(x0), n__incr(z0))) -> c6(INCR(cons(adx(x0), n__adx(incr(z0)))), ACTIVATE(n__adx(x0)))
   ADX(cons(n__adx(x0), n__adx(z0))) -> c6(INCR(cons(adx(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(x0)))
   ADX(cons(n__adx(x0), z0)) -> c6(INCR(cons(adx(x0), n__adx(z0))), ACTIVATE(n__adx(x0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) by 
   ADX(cons(x0, n__0)) -> c6(INCR(cons(x0, n__adx(0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(x0, n__adx(zeros))), ACTIVATE(x0))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(x0, n__adx(s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(x0, n__adx(incr(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(x0, n__adx(adx(z0)))), ACTIVATE(x0))
   ADX(cons(x0, z0)) -> c6(INCR(cons(x0, n__adx(z0))), ACTIVATE(x0))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_1, c7_2, c7_1, c6_2


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) by 
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(0, n__adx(incr(z0)))))
   ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(0, n__adx(adx(z0)))))
   ADX(cons(n__0, z0)) -> c6(INCR(cons(0, n__adx(z0))))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_1, c7_2, c7_1, c6_2


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) by 
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__zeros, n__incr(z0))) -> c6(INCR(cons(zeros, n__adx(incr(z0)))))
   ADX(cons(n__zeros, n__adx(z0))) -> c6(INCR(cons(zeros, n__adx(adx(z0)))))
   ADX(cons(n__zeros, z0)) -> c6(INCR(cons(zeros, n__adx(z0))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_1, c7_2, c7_1, c6_2


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) by 
   ADX(cons(n__s(x0), n__0)) -> c6(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c6(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c6(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__s(x0), n__incr(z0))) -> c6(INCR(cons(s(x0), n__adx(incr(z0)))))
   ADX(cons(n__s(x0), n__adx(z0))) -> c6(INCR(cons(s(x0), n__adx(adx(z0)))))
   ADX(cons(n__s(x0), z0)) -> c6(INCR(cons(s(x0), n__adx(z0))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) by 
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) by 
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) by 
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) by 
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__0, n__incr(z0))) -> c7(INCR(cons(0, n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__adx(z0))) -> c7(INCR(cons(0, n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, z0)) -> c7(INCR(cons(0, n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) by 
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__zeros, n__incr(z0))) -> c7(INCR(cons(zeros, n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__zeros, n__adx(z0))) -> c7(INCR(cons(zeros, n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__zeros, z0)) -> c7(INCR(cons(zeros, n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) by 
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__s(x0), n__incr(z0))) -> c7(INCR(cons(s(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__s(x0), n__adx(z0))) -> c7(INCR(cons(s(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__s(x0), z0)) -> c7(INCR(cons(s(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) by 
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(x0), n__incr(z0))) -> c7(INCR(cons(incr(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__incr(x0), n__adx(z0))) -> c7(INCR(cons(incr(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__incr(x0), z0)) -> c7(INCR(cons(incr(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) by 
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__adx(x0), n__incr(z0))) -> c7(INCR(cons(adx(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(x0), n__adx(z0))) -> c7(INCR(cons(adx(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__adx(x0), z0)) -> c7(INCR(cons(adx(x0), n__adx(z0))), ACTIVATE(z0))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))), ACTIVATE(n__0))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_2, c7_1, c6_2, c6_1


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

(145) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) by 
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))), ACTIVATE(n__s(z0)))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(x0, n__adx(incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(x0, n__adx(adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(x0, z0)) -> c7(INCR(cons(x0, n__adx(z0))), ACTIVATE(z0))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))), ACTIVATE(n__s(z0)))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))), ACTIVATE(n__0))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))), ACTIVATE(n__zeros))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))), ACTIVATE(n__s(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_1, c6_2, c6_1, c7_2


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

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_1, c6_2, c6_1, c7_2


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) by 
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c7(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(n__incr(z0), n__0)) -> c7(INCR(cons(incr(z0), n__adx(0))))
   ADX(cons(n__adx(z0), n__0)) -> c7(INCR(cons(adx(z0), n__adx(0))))
   ADX(cons(z0, n__0)) -> c7(INCR(cons(z0, n__adx(0))))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_1, c6_2, c6_1, c7_2


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

(151) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) by 
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c7(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__zeros)) -> c7(INCR(cons(incr(z0), n__adx(zeros))))
   ADX(cons(n__adx(z0), n__zeros)) -> c7(INCR(cons(adx(z0), n__adx(zeros))))
   ADX(cons(z0, n__zeros)) -> c7(INCR(cons(z0, n__adx(zeros))))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c7_1, c6_2, c6_1, c7_2


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) by 
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__0, n__s(x1))) -> c7(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c7(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c7(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(n__incr(z0), n__s(x1))) -> c7(INCR(cons(incr(z0), n__adx(s(x1)))))
   ADX(cons(n__adx(z0), n__s(x1))) -> c7(INCR(cons(adx(z0), n__adx(s(x1)))))
   ADX(cons(z0, n__s(x1))) -> c7(INCR(cons(z0, n__adx(s(x1)))))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(155) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0))) by ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
----------------------------------------

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(157) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0))) by ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
----------------------------------------

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(159) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) by ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
----------------------------------------

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(161) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) by ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
----------------------------------------

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(163) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) by ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
----------------------------------------

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(165) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) by ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
----------------------------------------

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
S tuples:
   INCR(cons(z0, z1)) -> c3(ACTIVATE(z0))
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c3_1, c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1


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

(167) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) by 
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
S tuples:
   INCR(cons(z0, z1)) -> c4(ACTIVATE(z1))
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   INCR_1, ACTIVATE_1, ADX_1

Compound Symbols:   c4_1, c16_1, c17_1, c6_2, c6_1, c7_2, c7_1, c3_1


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

(169) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) by 
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
S tuples:
   ACTIVATE(n__incr(z0)) -> c16(INCR(z0))
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c16_1, c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1


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

(171) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) by 
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(173) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) by ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
----------------------------------------

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(175) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) by ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
----------------------------------------

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(177) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) by ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
----------------------------------------

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(179) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) by ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
----------------------------------------

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(181) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) by ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
----------------------------------------

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(183) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) by ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
----------------------------------------

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(185) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) by ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
----------------------------------------

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(187) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) by ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
----------------------------------------

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(189) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1))))) by ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
----------------------------------------

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(191) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1))))) by ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
----------------------------------------

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(193) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1))))) by ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(n__0, n__adx(adx(z0)))))
----------------------------------------

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
   ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(n__0, n__adx(adx(z0)))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
   ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(n__0, n__adx(adx(z0)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(195) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1))))) by ADX(cons(n__s(z0), n__adx(z1))) -> c6(INCR(cons(n__s(z0), n__adx(adx(z1)))))
----------------------------------------

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
   ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(n__0, n__adx(adx(z0)))))
   ADX(cons(n__s(z0), n__adx(z1))) -> c6(INCR(cons(n__s(z0), n__adx(adx(z1)))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
   ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(n__0, n__adx(adx(z0)))))
   ADX(cons(n__s(z0), n__adx(z1))) -> c6(INCR(cons(n__s(z0), n__adx(adx(z1)))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(197) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) by ADX(cons(n__0, z0)) -> c6(INCR(cons(n__0, n__adx(z0))))
----------------------------------------

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
   ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(n__0, n__adx(adx(z0)))))
   ADX(cons(n__s(z0), n__adx(z1))) -> c6(INCR(cons(n__s(z0), n__adx(adx(z1)))))
   ADX(cons(n__0, z0)) -> c6(INCR(cons(n__0, n__adx(z0))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
   ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(n__0, n__adx(adx(z0)))))
   ADX(cons(n__s(z0), n__adx(z1))) -> c6(INCR(cons(n__s(z0), n__adx(adx(z1)))))
   ADX(cons(n__0, z0)) -> c6(INCR(cons(n__0, n__adx(z0))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1


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

(199) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) by ADX(cons(n__s(z0), z1)) -> c6(INCR(cons(n__s(z0), n__adx(z1))))
----------------------------------------

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__0) -> 0
   activate(n__zeros) -> zeros
   activate(n__s(z0)) -> s(z0)
   activate(n__incr(z0)) -> incr(z0)
   activate(n__adx(z0)) -> adx(z0)
   activate(z0) -> z0
   0 -> n__0
   zeros -> cons(n__0, n__zeros)
   zeros -> n__zeros
   s(z0) -> n__s(z0)
   incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1)))
   incr(z0) -> n__incr(z0)
   adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1))))
   adx(z0) -> n__adx(z0)
Tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(z0), n__adx(s(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(z0), n__adx(s(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))))
   ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))))
   ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(x1)))))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(x1)))))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
   ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(n__0, n__adx(adx(z0)))))
   ADX(cons(n__s(z0), n__adx(z1))) -> c6(INCR(cons(n__s(z0), n__adx(adx(z1)))))
   ADX(cons(n__0, z0)) -> c6(INCR(cons(n__0, n__adx(z0))))
   ADX(cons(n__s(z0), z1)) -> c6(INCR(cons(n__s(z0), n__adx(z1))))
S tuples:
   ACTIVATE(n__adx(z0)) -> c17(ADX(z0))
   ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0))
   ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(z0), n__adx(zeros))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(z0), n__adx(zeros))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(x0))
   ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(x1)))))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c6(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(x0))
   ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(x0))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(z0))
   ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(x1)))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0))
   ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c6(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c6(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))))
   ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0)))))
   ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1)))))
   ADX(cons(x0, n__incr(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE(n__incr(cons(z0, z1))))
   ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(x1)))), ACTIVATE(n__incr(x1)))
   ADX(cons(x0, n__adx(cons(z0, z1)))) -> c7(INCR(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE(n__adx(cons(z0, z1))))
   ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE(n__adx(z0)))
   ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(x1)))), ACTIVATE(n__adx(x1)))
   ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(x1))), ACTIVATE(x1))
   ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1))
   ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))))
   ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))))
   ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0))
   ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))))
   ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))))
   ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))))
   ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))))
   ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))))
   ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))))
   ADX(cons(n__incr(cons(z0, z1)), x1)) -> c7(INCR(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(x0), n__adx(0))))
   ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(x0), n__adx(zeros))))
   ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(x0), n__adx(s(z0)))))
   ADX(cons(n__adx(cons(z0, z1)), x1)) -> c7(INCR(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE(x1))
   ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(x0), n__adx(0))))
   ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(x0), n__adx(zeros))))
   ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(x0), n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))))
   ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))))
   ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros))))
   ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0)))))
   ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(z0), n__adx(n__0))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(z0), n__adx(n__0))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0))
   ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0))))
   ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0))))
   ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(n__0))))
   INCR(cons(n__incr(y0), z1)) -> c3(ACTIVATE(n__incr(y0)))
   INCR(cons(n__adx(y0), z1)) -> c3(ACTIVATE(n__adx(y0)))
   INCR(cons(z0, n__incr(y0))) -> c4(ACTIVATE(n__incr(y0)))
   INCR(cons(z0, n__adx(y0))) -> c4(ACTIVATE(n__adx(y0)))
   ACTIVATE(n__incr(cons(n__incr(y0), y1))) -> c16(INCR(cons(n__incr(y0), y1)))
   ACTIVATE(n__incr(cons(n__adx(y0), y1))) -> c16(INCR(cons(n__adx(y0), y1)))
   ACTIVATE(n__incr(cons(y0, n__incr(y1)))) -> c16(INCR(cons(y0, n__incr(y1))))
   ACTIVATE(n__incr(cons(y0, n__adx(y1)))) -> c16(INCR(cons(y0, n__adx(y1))))
   ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(n__0, n__adx(zeros))))
   ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(n__s(z0), n__adx(zeros))))
   ADX(cons(n__incr(z0), n__s(z1))) -> c6(INCR(cons(incr(z0), n__adx(n__s(z1)))), ACTIVATE(n__incr(z0)))
   ADX(cons(n__adx(z0), n__s(z1))) -> c6(INCR(cons(adx(z0), n__adx(n__s(z1)))), ACTIVATE(n__adx(z0)))
   ADX(cons(z0, n__s(z1))) -> c6(INCR(cons(z0, n__adx(n__s(z1)))), ACTIVATE(z0))
   ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(n__s(z0)))))
   ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(n__s(z0)))))
   ADX(cons(n__s(z0), n__s(z1))) -> c6(INCR(cons(s(z0), n__adx(n__s(z1)))))
   ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(n__0, n__adx(incr(z0)))))
   ADX(cons(n__s(z0), n__incr(z1))) -> c6(INCR(cons(n__s(z0), n__adx(incr(z1)))))
   ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(n__0, n__adx(adx(z0)))))
   ADX(cons(n__s(z0), n__adx(z1))) -> c6(INCR(cons(n__s(z0), n__adx(adx(z1)))))
   ADX(cons(n__0, z0)) -> c6(INCR(cons(n__0, n__adx(z0))))
   ADX(cons(n__s(z0), z1)) -> c6(INCR(cons(n__s(z0), n__adx(z1))))
K tuples:none
Defined Rule Symbols:   activate_1, 0, zeros, s_1, incr_1, adx_1

Defined Pair Symbols:   ACTIVATE_1, ADX_1, INCR_1

Compound Symbols:   c17_1, c6_2, c6_1, c7_2, c7_1, c3_1, c4_1, c16_1