KILLED
proof of input_e5GOlqMvww.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxWeightedTrs
    (7) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxWeightedTrs
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxTypedWeightedTrs
    (11) CompletionProof [UPPER BOUND(ID), 0 ms]
    (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (14) CpxRNTS
    (15) CompletionProof [UPPER BOUND(ID), 0 ms]
    (16) CpxTypedWeightedCompleteTrs
        (17) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (18) CpxTypedWeightedCompleteTrs
        (19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (20) CpxRNTS
        (21) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (22) CpxRNTS
        (23) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxRNTS
        (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (26) CpxRNTS
        (27) IntTrsBoundProof [UPPER BOUND(ID), 491 ms]
        (28) CpxRNTS
        (29) IntTrsBoundProof [UPPER BOUND(ID), 92 ms]
        (30) CpxRNTS
        (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (32) CpxRNTS
        (33) IntTrsBoundProof [UPPER BOUND(ID), 376 ms]
        (34) CpxRNTS
        (35) IntTrsBoundProof [UPPER BOUND(ID), 126 ms]
        (36) CpxRNTS
        (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (38) CpxRNTS
        (39) IntTrsBoundProof [UPPER BOUND(ID), 234 ms]
        (40) CpxRNTS
        (41) IntTrsBoundProof [UPPER BOUND(ID), 57 ms]
        (42) CpxRNTS
        (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (44) CpxRNTS
        (45) IntTrsBoundProof [UPPER BOUND(ID), 283 ms]
        (46) CpxRNTS
        (47) IntTrsBoundProof [UPPER BOUND(ID), 93 ms]
        (48) CpxRNTS
        (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (50) CpxRNTS
        (51) IntTrsBoundProof [UPPER BOUND(ID), 424 ms]
        (52) CpxRNTS
        (53) IntTrsBoundProof [UPPER BOUND(ID), 87 ms]
        (54) CpxRNTS
        (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (56) CpxRNTS
        (57) IntTrsBoundProof [UPPER BOUND(ID), 6262 ms]
        (58) CpxRNTS
        (59) IntTrsBoundProof [UPPER BOUND(ID), 3809 ms]
        (60) CpxRNTS
(61) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(62) CdtProblem
    (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 312 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 207 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 298 ms]
    (88) CdtProblem
    (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms]
    (92) CdtProblem
    (93) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 373 ms]
    (94) CdtProblem
    (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms]
    (98) CdtProblem
    (99) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 397 ms]
    (102) CdtProblem
    (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 459 ms]
    (110) CdtProblem
    (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 482 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms]
    (118) CdtProblem
    (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 530 ms]
    (124) CdtProblem
    (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 537 ms]
    (130) CdtProblem
    (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtRewritingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (134) CdtProblem
    (135) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (148) CdtProblem
    (149) CdtRewritingProof [BOTH BOUNDS(ID, ID), 6 ms]
    (150) CdtProblem
    (151) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtRewritingProof [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) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3 ms]
    (160) CdtProblem
    (161) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) 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:

   min(0, y) -> 0
   min(x, 0) -> 0
   min(s(x), s(y)) -> s(min(x, y))
   max(0, y) -> y
   max(x, 0) -> x
   max(s(x), s(y)) -> s(max(x, y))
   +(0, y) -> y
   +(s(x), y) -> s(+(x, y))
   -(x, 0) -> x
   -(s(x), s(y)) -> -(x, y)
   *(x, 0) -> 0
   *(x, s(y)) -> +(x, *(x, y))
   f(s(x)) -> f(-(max(*(s(x), s(x)), +(s(x), s(s(s(0))))), max(s(*(s(x), s(x))), +(s(x), s(s(s(s(0))))))))

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:

   min(0', y) -> 0'
   min(x, 0') -> 0'
   min(s(x), s(y)) -> s(min(x, y))
   max(0', y) -> y
   max(x, 0') -> x
   max(s(x), s(y)) -> s(max(x, y))
   +'(0', y) -> y
   +'(s(x), y) -> s(+'(x, y))
   -(x, 0') -> x
   -(s(x), s(y)) -> -(x, y)
   *'(x, 0') -> 0'
   *'(x, s(y)) -> +'(x, *'(x, y))
   f(s(x)) -> f(-(max(*'(s(x), s(x)), +'(s(x), s(s(s(0'))))), max(s(*'(s(x), s(x))), +'(s(x), s(s(s(s(0'))))))))

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:

   min(0, y) -> 0
   min(x, 0) -> 0
   min(s(x), s(y)) -> s(min(x, y))
   max(0, y) -> y
   max(x, 0) -> x
   max(s(x), s(y)) -> s(max(x, y))
   +(0, y) -> y
   +(s(x), y) -> s(+(x, y))
   -(x, 0) -> x
   -(s(x), s(y)) -> -(x, y)
   *(x, 0) -> 0
   *(x, s(y)) -> +(x, *(x, y))
   f(s(x)) -> f(-(max(*(s(x), s(x)), +(s(x), s(s(s(0))))), max(s(*(s(x), s(x))), +(s(x), s(s(s(s(0))))))))

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

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

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


The TRS R consists of the following rules:

   min(0, y) -> 0 [1]
   min(x, 0) -> 0 [1]
   min(s(x), s(y)) -> s(min(x, y)) [1]
   max(0, y) -> y [1]
   max(x, 0) -> x [1]
   max(s(x), s(y)) -> s(max(x, y)) [1]
   +(0, y) -> y [1]
   +(s(x), y) -> s(+(x, y)) [1]
   -(x, 0) -> x [1]
   -(s(x), s(y)) -> -(x, y) [1]
   *(x, 0) -> 0 [1]
   *(x, s(y)) -> +(x, *(x, y)) [1]
   f(s(x)) -> f(-(max(*(s(x), s(x)), +(s(x), s(s(s(0))))), max(s(*(s(x), s(x))), +(s(x), s(s(s(s(0)))))))) [1]

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

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

+ => plus
- => minus
* => times

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

(8)
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:

   min(0, y) -> 0 [1]
   min(x, 0) -> 0 [1]
   min(s(x), s(y)) -> s(min(x, y)) [1]
   max(0, y) -> y [1]
   max(x, 0) -> x [1]
   max(s(x), s(y)) -> s(max(x, y)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   minus(x, 0) -> x [1]
   minus(s(x), s(y)) -> minus(x, y) [1]
   times(x, 0) -> 0 [1]
   times(x, s(y)) -> plus(x, times(x, y)) [1]
   f(s(x)) -> f(minus(max(times(s(x), s(x)), plus(s(x), s(s(s(0))))), max(s(times(s(x), s(x))), plus(s(x), s(s(s(s(0)))))))) [1]

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

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

(10)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   min(0, y) -> 0 [1]
   min(x, 0) -> 0 [1]
   min(s(x), s(y)) -> s(min(x, y)) [1]
   max(0, y) -> y [1]
   max(x, 0) -> x [1]
   max(s(x), s(y)) -> s(max(x, y)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   minus(x, 0) -> x [1]
   minus(s(x), s(y)) -> minus(x, y) [1]
   times(x, 0) -> 0 [1]
   times(x, s(y)) -> plus(x, times(x, y)) [1]
   f(s(x)) -> f(minus(max(times(s(x), s(x)), plus(s(x), s(s(s(0))))), max(s(times(s(x), s(x))), plus(s(x), s(s(s(s(0)))))))) [1]

The TRS has the following type information:
min :: 0:s -> 0:s -> 0:s
0 :: 0:s
s :: 0:s -> 0:s
max :: 0:s -> 0:s -> 0:s
plus :: 0:s -> 0:s -> 0:s
minus :: 0:s -> 0:s -> 0:s
times :: 0:s -> 0:s -> 0:s
f :: 0:s -> f

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

(11) 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:

   minus(v0, v1) -> null_minus [0]
   f(v0) -> null_f [0]
   min(v0, v1) -> null_min [0]
   max(v0, v1) -> null_max [0]
   plus(v0, v1) -> null_plus [0]
   times(v0, v1) -> null_times [0]

And the following fresh constants:    null_minus, null_f, null_min, null_max, null_plus, null_times

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

(12)
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:

   min(0, y) -> 0 [1]
   min(x, 0) -> 0 [1]
   min(s(x), s(y)) -> s(min(x, y)) [1]
   max(0, y) -> y [1]
   max(x, 0) -> x [1]
   max(s(x), s(y)) -> s(max(x, y)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   minus(x, 0) -> x [1]
   minus(s(x), s(y)) -> minus(x, y) [1]
   times(x, 0) -> 0 [1]
   times(x, s(y)) -> plus(x, times(x, y)) [1]
   f(s(x)) -> f(minus(max(times(s(x), s(x)), plus(s(x), s(s(s(0))))), max(s(times(s(x), s(x))), plus(s(x), s(s(s(s(0)))))))) [1]
   minus(v0, v1) -> null_minus [0]
   f(v0) -> null_f [0]
   min(v0, v1) -> null_min [0]
   max(v0, v1) -> null_max [0]
   plus(v0, v1) -> null_plus [0]
   times(v0, v1) -> null_times [0]

The TRS has the following type information:
min :: 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times
0 :: 0:s:null_minus:null_min:null_max:null_plus:null_times
s :: 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times
max :: 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times
plus :: 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times
minus :: 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times
times :: 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times -> 0:s:null_minus:null_min:null_max:null_plus:null_times
f :: 0:s:null_minus:null_min:null_max:null_plus:null_times -> null_f
null_minus :: 0:s:null_minus:null_min:null_max:null_plus:null_times
null_f :: null_f
null_min :: 0:s:null_minus:null_min:null_max:null_plus:null_times
null_max :: 0:s:null_minus:null_min:null_max:null_plus:null_times
null_plus :: 0:s:null_minus:null_min:null_max:null_plus:null_times
null_times :: 0:s:null_minus:null_min:null_max:null_plus:null_times

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

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

   0 => 0
   null_minus => 0
   null_f => 0
   null_min => 0
   null_max => 0
   null_plus => 0
   null_times => 0

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

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 1 }-> f(minus(max(times(1 + x, 1 + x), plus(1 + x, 1 + (1 + (1 + 0)))), max(1 + times(1 + x, 1 + x), plus(1 + x, 1 + (1 + (1 + (1 + 0))))))) :|: x >= 0, z = 1 + x
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   max(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   max(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y
   max(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   max(z, z') -{ 1 }-> 1 + max(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   min(z, z') -{ 1 }-> 0 :|: y >= 0, z = 0, z' = y
   min(z, z') -{ 1 }-> 0 :|: x >= 0, z = x, z' = 0
   min(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   min(z, z') -{ 1 }-> 1 + min(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   minus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   minus(z, z') -{ 1 }-> minus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 1 }-> 1 + plus(x, y) :|: x >= 0, y >= 0, z = 1 + x, z' = y
   times(z, z') -{ 1 }-> plus(x, times(x, y)) :|: z' = 1 + y, x >= 0, y >= 0, z = x
   times(z, z') -{ 1 }-> 0 :|: x >= 0, z = x, z' = 0
   times(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1

Only complete derivations are relevant for the runtime complexity.

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

(15) 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:

   min_2
   f_1

(c) The following functions are completely defined:

   times_2
   minus_2
   max_2
   plus_2

Due to the following rules being added:

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

And the following fresh constants:    const

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

(16)
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:

   min(0, y) -> 0 [1]
   min(x, 0) -> 0 [1]
   min(s(x), s(y)) -> s(min(x, y)) [1]
   max(0, y) -> y [1]
   max(x, 0) -> x [1]
   max(s(x), s(y)) -> s(max(x, y)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   minus(x, 0) -> x [1]
   minus(s(x), s(y)) -> minus(x, y) [1]
   times(x, 0) -> 0 [1]
   times(x, s(y)) -> plus(x, times(x, y)) [1]
   f(s(x)) -> f(minus(max(times(s(x), s(x)), plus(s(x), s(s(s(0))))), max(s(times(s(x), s(x))), plus(s(x), s(s(s(s(0)))))))) [1]
   minus(v0, v1) -> 0 [0]

The TRS has the following type information:
min :: 0:s -> 0:s -> 0:s
0 :: 0:s
s :: 0:s -> 0:s
max :: 0:s -> 0:s -> 0:s
plus :: 0:s -> 0:s -> 0:s
minus :: 0:s -> 0:s -> 0:s
times :: 0:s -> 0:s -> 0:s
f :: 0:s -> f
const :: f

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

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

(18)
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:

   min(0, y) -> 0 [1]
   min(x, 0) -> 0 [1]
   min(s(x), s(y)) -> s(min(x, y)) [1]
   max(0, y) -> y [1]
   max(x, 0) -> x [1]
   max(s(x), s(y)) -> s(max(x, y)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   minus(x, 0) -> x [1]
   minus(s(x), s(y)) -> minus(x, y) [1]
   times(x, 0) -> 0 [1]
   times(x, s(0)) -> plus(x, 0) [2]
   times(x, s(s(y'))) -> plus(x, plus(x, times(x, y'))) [2]
   f(s(x)) -> f(minus(max(plus(s(x), times(s(x), x)), s(plus(x, s(s(s(0)))))), max(s(plus(s(x), times(s(x), x))), s(plus(x, s(s(s(s(0))))))))) [5]
   minus(v0, v1) -> 0 [0]

The TRS has the following type information:
min :: 0:s -> 0:s -> 0:s
0 :: 0:s
s :: 0:s -> 0:s
max :: 0:s -> 0:s -> 0:s
plus :: 0:s -> 0:s -> 0:s
minus :: 0:s -> 0:s -> 0:s
times :: 0:s -> 0:s -> 0:s
f :: 0:s -> f
const :: f

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

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

   0 => 0
   const => 0

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

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> f(minus(max(plus(1 + x, times(1 + x, x)), 1 + plus(x, 1 + (1 + (1 + 0)))), max(1 + plus(1 + x, times(1 + x, x)), 1 + plus(x, 1 + (1 + (1 + (1 + 0))))))) :|: x >= 0, z = 1 + x
   max(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   max(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y
   max(z, z') -{ 1 }-> 1 + max(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   min(z, z') -{ 1 }-> 0 :|: y >= 0, z = 0, z' = y
   min(z, z') -{ 1 }-> 0 :|: x >= 0, z = x, z' = 0
   min(z, z') -{ 1 }-> 1 + min(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   minus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   minus(z, z') -{ 1 }-> minus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y
   plus(z, z') -{ 1 }-> 1 + plus(x, y) :|: x >= 0, y >= 0, z = 1 + x, z' = y
   times(z, z') -{ 2 }-> plus(x, plus(x, times(x, y'))) :|: z' = 1 + (1 + y'), x >= 0, y' >= 0, z = x
   times(z, z') -{ 2 }-> plus(x, 0) :|: x >= 0, z' = 1 + 0, z = x
   times(z, z') -{ 1 }-> 0 :|: x >= 0, z = x, z' = 0


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

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

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 1 }-> 1 + max(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0


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

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

   { max }
   { minus }
   { min }
   { plus }
   { times }
   { f }

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

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 1 }-> 1 + max(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {max}, {minus}, {min}, {plus}, {times}, {f}

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

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

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 1 }-> 1 + max(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {max}, {minus}, {min}, {plus}, {times}, {f}

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 1 }-> 1 + max(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {max}, {minus}, {min}, {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: ?, size: O(n^1) [z + z']

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 1 }-> 1 + max(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {minus}, {min}, {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {minus}, {min}, {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {minus}, {min}, {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: ?, size: O(n^1) [z]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 1 }-> minus(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {min}, {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {min}, {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {min}, {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: ?, size: O(n^1) [z]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 1 }-> 1 + min(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {plus}, {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  plus: runtime: ?, size: O(n^1) [z + z']

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 5 }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + 0)))), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + plus(z - 1, 1 + (1 + (1 + (1 + 0))))))) :|: z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 }-> 1 + plus(z - 1, z') :|: z - 1 >= 0, z' >= 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 2 }-> plus(z, 0) :|: z >= 0, z' = 1 + 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  plus: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']

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

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

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

   f(z) -{ 5 + 2*z }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + s3), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + s4))) :|: s3 >= 0, s3 <= z - 1 + (1 + (1 + (1 + 0))), s4 >= 0, s4 <= z - 1 + (1 + (1 + (1 + (1 + 0)))), z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 + z }-> 1 + s1 :|: s1 >= 0, s1 <= z - 1 + z', z - 1 >= 0, z' >= 0
   times(z, z') -{ 3 + z }-> s2 :|: s2 >= 0, s2 <= z + 0, z >= 0, z' = 1 + 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  plus: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']

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

(51) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 5 + 2*z }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + s3), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + s4))) :|: s3 >= 0, s3 <= z - 1 + (1 + (1 + (1 + 0))), s4 >= 0, s4 <= z - 1 + (1 + (1 + (1 + (1 + 0)))), z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 + z }-> 1 + s1 :|: s1 >= 0, s1 <= z - 1 + z', z - 1 >= 0, z' >= 0
   times(z, z') -{ 3 + z }-> s2 :|: s2 >= 0, s2 <= z + 0, z >= 0, z' = 1 + 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {times}, {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  plus: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  times: runtime: ?, size: O(n^2) [z + 2*z*z']

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 5 + 2*z }-> f(minus(max(plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + s3), max(1 + plus(1 + (z - 1), times(1 + (z - 1), z - 1)), 1 + s4))) :|: s3 >= 0, s3 <= z - 1 + (1 + (1 + (1 + 0))), s4 >= 0, s4 <= z - 1 + (1 + (1 + (1 + (1 + 0)))), z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 + z }-> 1 + s1 :|: s1 >= 0, s1 <= z - 1 + z', z - 1 >= 0, z' >= 0
   times(z, z') -{ 3 + z }-> s2 :|: s2 >= 0, s2 <= z + 0, z >= 0, z' = 1 + 0
   times(z, z') -{ 2 }-> plus(z, plus(z, times(z, z' - 2))) :|: z >= 0, z' - 2 >= 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  plus: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  times: runtime: O(n^2) [4 + z + 2*z*z' + 4*z'], size: O(n^2) [z + 2*z*z']

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

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

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

   f(z) -{ 14 + s13 + s3 + s4 + 10*z + 4*z^2 }-> f(s14) :|: s8 >= 0, s8 <= 1 + (z - 1) + 2 * ((z - 1) * (1 + (z - 1))), s9 >= 0, s9 <= 1 + (z - 1) + s8, s10 >= 0, s10 <= 1 + s3 + s9, s11 >= 0, s11 <= 1 + (z - 1) + 2 * ((z - 1) * (1 + (z - 1))), s12 >= 0, s12 <= 1 + (z - 1) + s11, s13 >= 0, s13 <= 1 + s4 + (1 + s12), s14 >= 0, s14 <= s10, s3 >= 0, s3 <= z - 1 + (1 + (1 + (1 + 0))), s4 >= 0, s4 <= z - 1 + (1 + (1 + (1 + (1 + 0)))), z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 + z }-> 1 + s1 :|: s1 >= 0, s1 <= z - 1 + z', z - 1 >= 0, z' >= 0
   times(z, z') -{ 3 + z }-> s2 :|: s2 >= 0, s2 <= z + 0, z >= 0, z' = 1 + 0
   times(z, z') -{ -1*z + 2*z*z' + 4*z' }-> s7 :|: s5 >= 0, s5 <= z + 2 * ((z' - 2) * z), s6 >= 0, s6 <= z + s5, s7 >= 0, s7 <= z + s6, z >= 0, z' - 2 >= 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  plus: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  times: runtime: O(n^2) [4 + z + 2*z*z' + 4*z'], size: O(n^2) [z + 2*z*z']

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

(57) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 14 + s13 + s3 + s4 + 10*z + 4*z^2 }-> f(s14) :|: s8 >= 0, s8 <= 1 + (z - 1) + 2 * ((z - 1) * (1 + (z - 1))), s9 >= 0, s9 <= 1 + (z - 1) + s8, s10 >= 0, s10 <= 1 + s3 + s9, s11 >= 0, s11 <= 1 + (z - 1) + 2 * ((z - 1) * (1 + (z - 1))), s12 >= 0, s12 <= 1 + (z - 1) + s11, s13 >= 0, s13 <= 1 + s4 + (1 + s12), s14 >= 0, s14 <= s10, s3 >= 0, s3 <= z - 1 + (1 + (1 + (1 + 0))), s4 >= 0, s4 <= z - 1 + (1 + (1 + (1 + (1 + 0)))), z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 + z }-> 1 + s1 :|: s1 >= 0, s1 <= z - 1 + z', z - 1 >= 0, z' >= 0
   times(z, z') -{ 3 + z }-> s2 :|: s2 >= 0, s2 <= z + 0, z >= 0, z' = 1 + 0
   times(z, z') -{ -1*z + 2*z*z' + 4*z' }-> s7 :|: s5 >= 0, s5 <= z + 2 * ((z' - 2) * z), s6 >= 0, s6 <= z + s5, s7 >= 0, s7 <= z + s6, z >= 0, z' - 2 >= 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  plus: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  times: runtime: O(n^2) [4 + z + 2*z*z' + 4*z'], size: O(n^2) [z + 2*z*z']
  f: runtime: ?, size: O(1) [0]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   f(z) -{ 14 + s13 + s3 + s4 + 10*z + 4*z^2 }-> f(s14) :|: s8 >= 0, s8 <= 1 + (z - 1) + 2 * ((z - 1) * (1 + (z - 1))), s9 >= 0, s9 <= 1 + (z - 1) + s8, s10 >= 0, s10 <= 1 + s3 + s9, s11 >= 0, s11 <= 1 + (z - 1) + 2 * ((z - 1) * (1 + (z - 1))), s12 >= 0, s12 <= 1 + (z - 1) + s11, s13 >= 0, s13 <= 1 + s4 + (1 + s12), s14 >= 0, s14 <= s10, s3 >= 0, s3 <= z - 1 + (1 + (1 + (1 + 0))), s4 >= 0, s4 <= z - 1 + (1 + (1 + (1 + (1 + 0)))), z - 1 >= 0
   max(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   max(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   max(z, z') -{ 2 + z' }-> 1 + s :|: s >= 0, s <= z' - 1 + (z - 1), z - 1 >= 0, z' - 1 >= 0
   min(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   min(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   min(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 + z' }-> s' :|: s' >= 0, s' <= z - 1, z - 1 >= 0, z' - 1 >= 0
   minus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   minus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   plus(z, z') -{ 1 + z }-> 1 + s1 :|: s1 >= 0, s1 <= z - 1 + z', z - 1 >= 0, z' >= 0
   times(z, z') -{ 3 + z }-> s2 :|: s2 >= 0, s2 <= z + 0, z >= 0, z' = 1 + 0
   times(z, z') -{ -1*z + 2*z*z' + 4*z' }-> s7 :|: s5 >= 0, s5 <= z + 2 * ((z' - 2) * z), s6 >= 0, s6 <= z + s5, s7 >= 0, s7 <= z + s6, z >= 0, z' - 2 >= 0
   times(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0

Function symbols to be analyzed: {f}
Previous analysis results are:
  max: runtime: O(n^1) [2 + z'], size: O(n^1) [z + z']
  minus: runtime: O(n^1) [1 + z'], size: O(n^1) [z]
  min: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  plus: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  times: runtime: O(n^2) [4 + z + 2*z*z' + 4*z'], size: O(n^2) [z + 2*z*z']
  f: runtime: INF, size: O(1) [0]

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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   min(0, z0) -> 0
   min(z0, 0) -> 0
   min(s(z0), s(z1)) -> s(min(z0, z1))
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   f(s(z0)) -> f(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))))
Tuples:
   MIN(0, z0) -> c
   MIN(z0, 0) -> c1
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(0, z0) -> c3
   MAX(z0, 0) -> c4
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(0, z0) -> c6
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(z0, 0) -> c8
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, 0) -> c10
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
S tuples:
   MIN(0, z0) -> c
   MIN(z0, 0) -> c1
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(0, z0) -> c3
   MAX(z0, 0) -> c4
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(0, z0) -> c6
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(z0, 0) -> c8
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, 0) -> c10
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
K tuples:none
Defined Rule Symbols:   min_2, max_2, +_2, -_2, *_2, f_1

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c, c1, c2_1, c3, c4, c5_1, c6, c7_1, c8, c9_1, c10, c11_2, c12_4, c13_4, c14_4, c15_4


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

(63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing nodes:
   -'(z0, 0) -> c8
   +'(0, z0) -> c6
   MIN(z0, 0) -> c1
   MAX(0, z0) -> c3
   MIN(0, z0) -> c
   MAX(z0, 0) -> c4
   *'(z0, 0) -> c10

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   min(0, z0) -> 0
   min(z0, 0) -> 0
   min(s(z0), s(z1)) -> s(min(z0, z1))
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   f(s(z0)) -> f(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
S tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
K tuples:none
Defined Rule Symbols:   min_2, max_2, +_2, -_2, *_2, f_1

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4


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

(65) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   min(0, z0) -> 0
   min(z0, 0) -> 0
   min(s(z0), s(z1)) -> s(min(z0, z1))
   f(s(z0)) -> f(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
S tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
K tuples:none
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4


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

(67) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(*(x_1, x_2)) = 0
   POL(*'(x_1, x_2)) = 0
   POL(+(x_1, x_2)) = 0
   POL(+'(x_1, x_2)) = 0
   POL(-(x_1, x_2)) = [1]
   POL(-'(x_1, x_2)) = 0
   POL(0) = 0
   POL(F(x_1)) = 0
   POL(MAX(x_1, x_2)) = 0
   POL(MIN(x_1, x_2)) = x_1 + x_2
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c15(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c2(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(max(x_1, x_2)) = [1]
   POL(s(x_1)) = [1] + x_1

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0))) by 
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c13_4, c14_4, c15_4, c12_4


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0))))) by 
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c14_4, c15_4, c12_4, c13_4


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0))) by 
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c15_4, c12_4, c13_4, c14_4


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0)))))) by 
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4


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

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0))) by 
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4, c12_1


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

(79) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
We considered the (Usable) Rules:none
And the Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(*(x_1, x_2)) = 0
   POL(*'(x_1, x_2)) = x_1
   POL(+(x_1, x_2)) = 0
   POL(+'(x_1, x_2)) = 0
   POL(-(x_1, x_2)) = [1]
   POL(-'(x_1, x_2)) = 0
   POL(0) = 0
   POL(F(x_1)) = [1]
   POL(MAX(x_1, x_2)) = 0
   POL(MIN(x_1, x_2)) = 0
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c12(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c15(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c2(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(max(x_1, x_2)) = [1]
   POL(s(x_1)) = 0

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4, c12_1


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1))) by 
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4, c12_1


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0))) by 
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), s(+(z1, s(s(s(0)))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4, c12_1, c12_2


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

(85) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4, c12_1, c_1


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

(87) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
We considered the (Usable) Rules:none
And the Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(*(x_1, x_2)) = 0
   POL(*'(x_1, x_2)) = x_1
   POL(+(x_1, x_2)) = 0
   POL(+'(x_1, x_2)) = 0
   POL(-(x_1, x_2)) = [1]
   POL(-'(x_1, x_2)) = 0
   POL(0) = 0
   POL(F(x_1)) = [1]
   POL(MAX(x_1, x_2)) = 0
   POL(MIN(x_1, x_2)) = 0
   POL(c(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c12(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c15(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c2(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(max(x_1, x_2)) = [1]
   POL(s(x_1)) = 0

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c13_4, c14_4, c15_4, c12_1, c_1


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1))) by 
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c13_4, c14_4, c15_4, c12_4, c12_1, c_1


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0))))) by 
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c13_4, c14_4, c15_4, c12_4, c12_1, c_1, c13_1


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

(93) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
We considered the (Usable) Rules:none
And the Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(*(x_1, x_2)) = 0
   POL(*'(x_1, x_2)) = x_1
   POL(+(x_1, x_2)) = 0
   POL(+'(x_1, x_2)) = 0
   POL(-(x_1, x_2)) = [1]
   POL(-'(x_1, x_2)) = 0
   POL(0) = 0
   POL(F(x_1)) = [1]
   POL(MAX(x_1, x_2)) = 0
   POL(MIN(x_1, x_2)) = 0
   POL(c(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c12(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c13(x_1)) = x_1
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c15(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c2(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(max(x_1, x_2)) = [1]
   POL(s(x_1)) = 0

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c13_4, c14_4, c15_4, c12_4, c12_1, c_1, c13_1


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0))))) by 
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c13_4, c14_4, c15_4, c12_4, c12_1, c_1, c13_1


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0))))) by 
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), s(+(z1, s(s(s(0)))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c13_4, c14_4, c15_4, c12_4, c12_1, c_1, c13_1, c13_3


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

(99) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c13_4, c14_4, c15_4, c12_4, c12_1, c_1, c13_1, c1_1


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

(101) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
We considered the (Usable) Rules:none
And the Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(*(x_1, x_2)) = 0
   POL(*'(x_1, x_2)) = x_1
   POL(+(x_1, x_2)) = 0
   POL(+'(x_1, x_2)) = 0
   POL(-(x_1, x_2)) = [1]
   POL(-'(x_1, x_2)) = 0
   POL(0) = 0
   POL(F(x_1)) = [1]
   POL(MAX(x_1, x_2)) = 0
   POL(MIN(x_1, x_2)) = 0
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c12(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c13(x_1)) = x_1
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c15(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c2(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(max(x_1, x_2)) = [1]
   POL(s(x_1)) = 0

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c13_4, c14_4, c15_4, c12_4, c12_1, c_1, c13_1, c1_1


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0))))) by 
   F(s(z0)) -> c13(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(+(s(z0), *(s(z0), z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c14_4, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0))) by 
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c14_4, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_2


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

(107) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c14_4, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c3_1


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

(109) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
We considered the (Usable) Rules:none
And the Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(*(x_1, x_2)) = 0
   POL(*'(x_1, x_2)) = x_1
   POL(+(x_1, x_2)) = 0
   POL(+'(x_1, x_2)) = 0
   POL(-(x_1, x_2)) = [1]
   POL(-'(x_1, x_2)) = 0
   POL(0) = 0
   POL(F(x_1)) = [1]
   POL(MAX(x_1, x_2)) = 0
   POL(MIN(x_1, x_2)) = 0
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c12(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c13(x_1)) = x_1
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c15(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c2(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(max(x_1, x_2)) = [1]
   POL(s(x_1)) = 0

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c14_4, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c3_1


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1))) by 
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c14_4, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c3_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0))) by 
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), s(+(z1, s(s(s(0)))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c14_4, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c3_1, c14_1


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

(115) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
We considered the (Usable) Rules:none
And the Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(*(x_1, x_2)) = 0
   POL(*'(x_1, x_2)) = x_1
   POL(+(x_1, x_2)) = 0
   POL(+'(x_1, x_2)) = 0
   POL(-(x_1, x_2)) = [1]
   POL(-'(x_1, x_2)) = 0
   POL(0) = 0
   POL(F(x_1)) = [1]
   POL(MAX(x_1, x_2)) = 0
   POL(MIN(x_1, x_2)) = 0
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c12(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c13(x_1)) = x_1
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c15(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c2(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(max(x_1, x_2)) = [1]
   POL(s(x_1)) = 0

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c14_4, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c3_1, c14_1


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1))) by 
   F(s(z0)) -> c14(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(+(s(z0), *(s(z0), z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0)))))) by 
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_3


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

(121) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c4_1


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

(123) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
We considered the (Usable) Rules:none
And the Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(*(x_1, x_2)) = 0
   POL(*'(x_1, x_2)) = x_1
   POL(+(x_1, x_2)) = 0
   POL(+'(x_1, x_2)) = 0
   POL(-(x_1, x_2)) = [1]
   POL(-'(x_1, x_2)) = 0
   POL(0) = 0
   POL(F(x_1)) = [1]
   POL(MAX(x_1, x_2)) = 0
   POL(MIN(x_1, x_2)) = 0
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c12(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c13(x_1)) = x_1
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c15(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c2(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(max(x_1, x_2)) = [1]
   POL(s(x_1)) = 0

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c4_1


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0)))))) by 
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c4_1


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0)))))) by 
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), s(+(z1, s(s(s(0)))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c4_1, c15_1


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

(129) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
We considered the (Usable) Rules:none
And the Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(*(x_1, x_2)) = 0
   POL(*'(x_1, x_2)) = x_1
   POL(+(x_1, x_2)) = 0
   POL(+'(x_1, x_2)) = 0
   POL(-(x_1, x_2)) = [1]
   POL(-'(x_1, x_2)) = 0
   POL(0) = 0
   POL(F(x_1)) = [1]
   POL(MAX(x_1, x_2)) = 0
   POL(MIN(x_1, x_2)) = 0
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c12(x_1)) = x_1
   POL(c12(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c13(x_1)) = x_1
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c15(x_1)) = x_1
   POL(c15(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c2(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(max(x_1, x_2)) = [1]
   POL(s(x_1)) = 0

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c15_4, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c4_1, c15_1


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0)))))) by 
   F(s(z0)) -> c15(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(+(s(z0), *(s(z0), z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1


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

(133) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(x0)) -> c12(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), *'(s(x0), s(x0))) by F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1


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

(135) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0))) by F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
----------------------------------------

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1


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

(137) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0)))) by F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
----------------------------------------

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1


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

(139) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1))) by F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
----------------------------------------

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
K tuples:
   MIN(s(z0), s(z1)) -> c2(MIN(z0, z1))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MIN_2, MAX_2, +'_2, -'_2, *'_2, F_1

Compound Symbols:   c2_1, c5_1, c7_1, c9_1, c11_2, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1


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

(141) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MIN(s(z0), s(z1)) -> c2(MIN(z0, z1)) by 
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MAX_2, +'_2, -'_2, *'_2, F_1, MIN_2

Compound Symbols:   c5_1, c7_1, c9_1, c11_2, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1


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

(143) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0))) by F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
----------------------------------------

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MAX_2, +'_2, -'_2, *'_2, F_1, MIN_2

Compound Symbols:   c5_1, c7_1, c9_1, c11_2, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1


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

(145) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1))) by F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
----------------------------------------

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MAX_2, +'_2, -'_2, *'_2, F_1, MIN_2

Compound Symbols:   c5_1, c7_1, c9_1, c11_2, c12_4, c12_1, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1


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

(147) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))) by F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
----------------------------------------

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MAX_2, +'_2, -'_2, *'_2, F_1, MIN_2

Compound Symbols:   c5_1, c7_1, c9_1, c11_2, c12_4, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1, c12_1


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

(149) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0))) by F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
----------------------------------------

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MAX_2, +'_2, -'_2, *'_2, F_1, MIN_2

Compound Symbols:   c5_1, c7_1, c9_1, c11_2, c12_4, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1, c12_1


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

(151) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0))) by F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
----------------------------------------

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MAX_2, +'_2, -'_2, *'_2, F_1, MIN_2

Compound Symbols:   c5_1, c7_1, c9_1, c11_2, c12_4, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1, c12_1


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

(153) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(s(z1))) -> c12(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1)))) by F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
----------------------------------------

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MAX_2, +'_2, -'_2, *'_2, F_1, MIN_2

Compound Symbols:   c5_1, c7_1, c9_1, c11_2, c12_4, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1, c12_1


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

(155) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0))) by F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
----------------------------------------

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MAX_2, +'_2, -'_2, *'_2, F_1, MIN_2

Compound Symbols:   c5_1, c7_1, c9_1, c11_2, c12_4, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1, c12_1


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

(157) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0))) by F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
----------------------------------------

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
S tuples:
   MAX(s(z0), s(z1)) -> c5(MAX(z0, z1))
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   MAX_2, +'_2, -'_2, *'_2, F_1, MIN_2

Compound Symbols:   c5_1, c7_1, c9_1, c11_2, c12_4, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1, c12_1


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

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

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MAX(s(s(y0)), s(s(y1))) -> c5(MAX(s(y0), s(y1)))
S tuples:
   +'(s(z0), z1) -> c7(+'(z0, z1))
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MAX(s(s(y0)), s(s(y1))) -> c5(MAX(s(y0), s(y1)))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   +'_2, -'_2, *'_2, F_1, MIN_2, MAX_2

Compound Symbols:   c7_1, c9_1, c11_2, c12_4, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1, c12_1, c5_1


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

(161) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace +'(s(z0), z1) -> c7(+'(z0, z1)) by 
   +'(s(s(y0)), z1) -> c7(+'(s(y0), z1))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MAX(s(s(y0)), s(s(y1))) -> c5(MAX(s(y0), s(y1)))
   +'(s(s(y0)), z1) -> c7(+'(s(y0), z1))
S tuples:
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), +'(s(0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), +'(s(0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MAX(s(s(y0)), s(s(y1))) -> c5(MAX(s(y0), s(y1)))
   +'(s(s(y0)), z1) -> c7(+'(s(y0), z1))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   -'_2, *'_2, F_1, MIN_2, MAX_2, +'_2

Compound Symbols:   c9_1, c11_2, c12_4, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1, c12_1, c5_1, c7_1


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

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   *(z0, 0) -> 0
   *(z0, s(z1)) -> +(z0, *(z0, z1))
   +(0, z0) -> z0
   +(s(z0), z1) -> s(+(z0, z1))
   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   max(0, z0) -> z0
   max(z0, 0) -> z0
   max(s(z0), s(z1)) -> s(max(z0, z1))
Tuples:
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(-'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0)))))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MAX(s(s(y0)), s(s(y1))) -> c5(MAX(s(y0), s(y1)))
   +'(s(s(y0)), z1) -> c7(+'(s(y0), z1))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))
S tuples:
   -'(s(z0), s(z1)) -> c9(-'(z0, z1))
   *'(z0, s(z1)) -> c11(+'(z0, *(z0, z1)), *'(z0, z1))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c12(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c12(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c12(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c13(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), +'(s(x0), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(s(z0))) -> c13(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), +'(s(s(z0)), s(s(s(0)))))
   F(s(z1)) -> c13(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), +'(s(z1), s(s(s(0)))))
   F(s(z0)) -> c13(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), +'(s(z0), s(s(s(0)))))
   F(s(s(z1))) -> c13(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), +'(s(s(z1)), s(s(s(0)))))
   F(s(x0)) -> c14(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), *'(s(x0), s(x0)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z1))) -> c14(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c14(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(0)) -> c14(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c14(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z1)) -> c14(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), *'(s(z1), s(z1)))
   F(s(z0)) -> c14(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c14(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z1))) -> c14(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), *'(s(s(z1)), s(s(z1))))
   F(s(x0)) -> c15(F(-(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), s(max(*(s(x0), s(x0)), +(x0, s(s(s(s(0))))))))), -'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))), MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))), +'(s(x0), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), s(+(z1, s(s(s(s(0))))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), +(s(z1), s(s(s(0))))), max(s(+(s(z1), *(s(z1), z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(s(z0))) -> c15(F(-(max(*(s(s(z0)), s(s(z0))), s(s(+(z0, s(s(s(0))))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0)))))), +'(s(s(z0)), s(s(s(s(0))))))
   F(s(z1)) -> c15(F(-(max(+(s(z1), *(s(z1), z1)), s(+(z1, s(s(s(0)))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))))), -'(max(*(s(z1), s(z1)), +(s(z1), s(s(s(0))))), max(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0))))))), MAX(s(*(s(z1), s(z1))), +(s(z1), s(s(s(s(0)))))), +'(s(z1), s(s(s(s(0))))))
   F(s(z0)) -> c15(F(-(max(s(+(z0, *(s(z0), z0))), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0)))))), +'(s(z0), s(s(s(s(0))))))
   F(s(s(z1))) -> c15(F(-(max(+(s(s(z1)), +(s(s(z1)), *(s(s(z1)), z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))))), -'(max(*(s(s(z1)), s(s(z1))), +(s(s(z1)), s(s(s(0))))), max(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0))))))), MAX(s(*(s(s(z1)), s(s(z1)))), +(s(s(z1)), s(s(s(s(0)))))), +'(s(s(z1)), s(s(s(s(0))))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), s(max(*(s(z0), s(z0)), +(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), s(s(+(z0, s(s(s(s(0)))))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(+(s(z0), *(s(z0), z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(+(s(z0), *(s(z0), z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), s(+(z0, s(s(s(s(0))))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(s(+(z0, *(s(z0), z0)))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   F(s(s(z0))) -> c12(F(-(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(+(s(s(z0)), +(s(s(z0)), *(s(s(z0)), z0)))), +(s(s(z0)), s(s(s(s(0)))))))), -'(max(*(s(s(z0)), s(s(z0))), +(s(s(z0)), s(s(s(0))))), max(s(*(s(s(z0)), s(s(z0)))), +(s(s(z0)), s(s(s(s(0))))))), MAX(*(s(s(z0)), s(s(z0))), s(+(s(z0), s(s(s(0)))))), *'(s(s(z0)), s(s(z0))))
   F(s(0)) -> c12(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), s(+(0, s(s(s(0)))))), *'(s(0), s(0)))
   F(s(z0)) -> c12(F(-(max(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), max(s(+(s(z0), *(s(z0), z0))), +(s(z0), s(s(s(s(0)))))))), -'(max(*(s(z0), s(z0)), +(s(z0), s(s(s(0))))), max(s(*(s(z0), s(z0))), +(s(z0), s(s(s(s(0))))))), MAX(*(s(z0), s(z0)), s(+(z0, s(s(s(0)))))), *'(s(z0), s(z0)))
   MAX(s(s(y0)), s(s(y1))) -> c5(MAX(s(y0), s(y1)))
   +'(s(s(y0)), z1) -> c7(+'(s(y0), z1))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))))
   F(s(0)) -> c13(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))))
   F(s(0)) -> c13(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(*(s(0), s(0)), +(s(0), s(s(s(0))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), s(s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(+(s(0), 0)), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))
   F(s(0)) -> c15(F(-(max(*(s(0), s(0)), s(s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))
   F(s(0)) -> c15(F(-(max(+(s(0), 0), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))), -'(max(*(s(0), s(0)), +(s(0), s(s(s(0))))), max(s(*(s(0), s(0))), +(s(0), s(s(s(s(0))))))), MAX(s(*(s(0), s(0))), +(s(0), s(s(s(s(0)))))))
K tuples:
   F(s(x0)) -> c12(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c13(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c1(MAX(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))))
   F(s(x0)) -> c1(+'(s(x0), s(s(s(0)))))
   F(s(x0)) -> c3(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c3(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c14(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   F(s(x0)) -> c4(MAX(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0)))))))
   F(s(x0)) -> c4(+'(s(x0), s(s(s(s(0))))))
   F(s(x0)) -> c15(-'(max(*(s(x0), s(x0)), +(s(x0), s(s(s(0))))), max(s(*(s(x0), s(x0))), +(s(x0), s(s(s(s(0))))))))
   MIN(s(s(y0)), s(s(y1))) -> c2(MIN(s(y0), s(y1)))
Defined Rule Symbols:   *_2, +_2, -_2, max_2

Defined Pair Symbols:   -'_2, *'_2, F_1, MIN_2, MAX_2, +'_2

Compound Symbols:   c9_1, c11_2, c12_4, c_1, c13_4, c13_1, c1_1, c14_4, c3_1, c14_1, c15_4, c4_1, c15_1, c2_1, c12_1, c5_1, c7_1, c13_3, c15_3