KILLED
proof of input_R9xSr9hlMt.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(6) CdtProblem
    (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxRelTRS
    (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxRelTRS
    (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) typed CpxTrs
    (13) OrderProof [LOWER BOUND(ID), 18 ms]
    (14) typed CpxTrs
    (15) RewriteLemmaProof [LOWER BOUND(ID), 473 ms]
    (16) BEST
        (17) proven lower bound
            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
            (19) BOUNDS(n^1, INF)
        (20) typed CpxTrs
            (21) RewriteLemmaProof [LOWER BOUND(ID), 184 ms]
            (22) BOUNDS(1, INF)
(23) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(24) CpxWeightedTrs
    (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CpxTypedWeightedTrs
    (27) CompletionProof [UPPER BOUND(ID), 0 ms]
    (28) CpxTypedWeightedCompleteTrs
        (29) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (30) CpxTypedWeightedCompleteTrs
        (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (32) CpxRNTS
        (33) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (34) CpxRNTS
        (35) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (36) CpxRNTS
        (37) ResultPropagationProof [UPPER BOUND(ID), 1 ms]
        (38) CpxRNTS
        (39) IntTrsBoundProof [UPPER BOUND(ID), 842 ms]
        (40) CpxRNTS
        (41) IntTrsBoundProof [UPPER BOUND(ID), 331 ms]
        (42) CpxRNTS
    (43) CompletionProof [UPPER BOUND(ID), 0 ms]
    (44) CpxTypedWeightedCompleteTrs
        (45) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (46) CpxRNTS
(47) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(48) CdtProblem
    (49) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CpxTRS
        (53) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (54) CpxTRS
        (55) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (56) CpxWeightedTrs
            (57) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (58) CpxTypedWeightedTrs
            (59) CompletionProof [UPPER BOUND(ID), 0 ms]
            (60) CpxTypedWeightedCompleteTrs
                (61) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
                (62) CpxTypedWeightedCompleteTrs
                (63) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (64) CpxRNTS
                (65) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
                (66) CpxRNTS
                (67) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
                (68) CpxRNTS
                (69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (70) CpxRNTS
                (71) IntTrsBoundProof [UPPER BOUND(ID), 898 ms]
                (72) CpxRNTS
                (73) IntTrsBoundProof [UPPER BOUND(ID), 348 ms]
                (74) CpxRNTS
            (75) CompletionProof [UPPER BOUND(ID), 0 ms]
            (76) CpxTypedWeightedCompleteTrs
                (77) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (78) CpxRNTS
    (79) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 31 ms]
    (80) CdtProblem
        (81) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 39 ms]
        (90) CdtProblem
        (91) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 7 ms]
        (96) CdtProblem
        (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 40 ms]
        (100) CdtProblem
        (101) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 172 ms]
        (102) CdtProblem
        (103) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 301 ms]
        (106) CdtProblem
        (107) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 529 ms]
        (108) CdtProblem
        (109) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1104 ms]
        (110) CdtProblem
        (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2019 ms]
        (114) CdtProblem
        (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 38 ms]
        (116) CdtProblem
        (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2694 ms]
        (118) CdtProblem
        (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 5512 ms]
        (120) CdtProblem
        (121) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 9634 ms]
        (122) CdtProblem
        (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 143 ms]
        (124) CdtProblem
        (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 13.1 s]
        (126) CdtProblem
        (127) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 23.1 s]
        (128) 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:

   f(0, 1, x) -> f(g(x), g(x), x)
   f(g(x), y, z) -> g(f(x, y, z))
   f(x, g(y), z) -> g(f(x, y, z))
   f(x, y, g(z)) -> g(f(x, y, z))

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:

   f(0', 1', x) -> f(g(x), g(x), x)
   f(g(x), y, z) -> g(f(x, y, z))
   f(x, g(y), z) -> g(f(x, y, z))
   f(x, y, g(z)) -> g(f(x, y, z))

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:

   f(0, 1, x) -> f(g(x), g(x), x)
   f(g(x), y, z) -> g(f(x, y, z))
   f(x, g(y), z) -> g(f(x, y, z))
   f(x, y, g(z)) -> g(f(x, y, z))

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

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

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0, 1, z0) -> f(g(z0), g(z0), z0)
   f(g(z0), z1, z2) -> g(f(z0, z1, z2))
   f(z0, g(z1), z2) -> g(f(z0, z1, z2))
   f(z0, z1, g(z2)) -> g(f(z0, z1, z2))
Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
S tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
K tuples:none
Defined Rule Symbols:   f_3

Defined Pair Symbols:   F_3

Compound Symbols:   c_1, c1_1, c2_1, c3_1


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

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

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


The TRS R consists of the following rules:

   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))

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

   f(0, 1, z0) -> f(g(z0), g(z0), z0)
   f(g(z0), z1, z2) -> g(f(z0, z1, z2))
   f(z0, g(z1), z2) -> g(f(z0, z1, z2))
   f(z0, z1, g(z2)) -> g(f(z0, z1, z2))

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

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

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


The TRS R consists of the following rules:

   F(0', 1', z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))

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

   f(0', 1', z0) -> f(g(z0), g(z0), z0)
   f(g(z0), z1, z2) -> g(f(z0, z1, z2))
   f(z0, g(z1), z2) -> g(f(z0, z1, z2))
   f(z0, z1, g(z2)) -> g(f(z0, z1, z2))

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

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

(12)
Obligation:
Innermost TRS:
Rules:
F(0', 1', z0) -> c(F(g(z0), g(z0), z0))
F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
f(0', 1', z0) -> f(g(z0), g(z0), z0)
f(g(z0), z1, z2) -> g(f(z0, z1, z2))
f(z0, g(z1), z2) -> g(f(z0, z1, z2))
f(z0, z1, g(z2)) -> g(f(z0, z1, z2))

Types:
F :: 0':1':g -> 0':1':g -> 0':1':g -> c:c1:c2:c3
0' :: 0':1':g
1' :: 0':1':g
c :: c:c1:c2:c3 -> c:c1:c2:c3
g :: 0':1':g -> 0':1':g
c1 :: c:c1:c2:c3 -> c:c1:c2:c3
c2 :: c:c1:c2:c3 -> c:c1:c2:c3
c3 :: c:c1:c2:c3 -> c:c1:c2:c3
f :: 0':1':g -> 0':1':g -> 0':1':g -> 0':1':g
hole_c:c1:c2:c31_4 :: c:c1:c2:c3
hole_0':1':g2_4 :: 0':1':g
gen_c:c1:c2:c33_4 :: Nat -> c:c1:c2:c3
gen_0':1':g4_4 :: Nat -> 0':1':g

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

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
F, f
----------------------------------------

(14)
Obligation:
Innermost TRS:
Rules:
F(0', 1', z0) -> c(F(g(z0), g(z0), z0))
F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
f(0', 1', z0) -> f(g(z0), g(z0), z0)
f(g(z0), z1, z2) -> g(f(z0, z1, z2))
f(z0, g(z1), z2) -> g(f(z0, z1, z2))
f(z0, z1, g(z2)) -> g(f(z0, z1, z2))

Types:
F :: 0':1':g -> 0':1':g -> 0':1':g -> c:c1:c2:c3
0' :: 0':1':g
1' :: 0':1':g
c :: c:c1:c2:c3 -> c:c1:c2:c3
g :: 0':1':g -> 0':1':g
c1 :: c:c1:c2:c3 -> c:c1:c2:c3
c2 :: c:c1:c2:c3 -> c:c1:c2:c3
c3 :: c:c1:c2:c3 -> c:c1:c2:c3
f :: 0':1':g -> 0':1':g -> 0':1':g -> 0':1':g
hole_c:c1:c2:c31_4 :: c:c1:c2:c3
hole_0':1':g2_4 :: 0':1':g
gen_c:c1:c2:c33_4 :: Nat -> c:c1:c2:c3
gen_0':1':g4_4 :: Nat -> 0':1':g


Generator Equations:
gen_c:c1:c2:c33_4(0) <=> hole_c:c1:c2:c31_4
gen_c:c1:c2:c33_4(+(x, 1)) <=> c(gen_c:c1:c2:c33_4(x))
gen_0':1':g4_4(0) <=> 1'
gen_0':1':g4_4(+(x, 1)) <=> g(gen_0':1':g4_4(x))


The following defined symbols remain to be analysed:
F, f
----------------------------------------

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
F(gen_0':1':g4_4(+(1, n6_4)), gen_0':1':g4_4(b), gen_0':1':g4_4(c)) -> *5_4, rt in Omega(n6_4)

Induction Base:
F(gen_0':1':g4_4(+(1, 0)), gen_0':1':g4_4(b), gen_0':1':g4_4(c))

Induction Step:
F(gen_0':1':g4_4(+(1, +(n6_4, 1))), gen_0':1':g4_4(b), gen_0':1':g4_4(c)) ->_R^Omega(1)
c1(F(gen_0':1':g4_4(+(1, n6_4)), gen_0':1':g4_4(b), gen_0':1':g4_4(c))) ->_IH
c1(*5_4)

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

(16)
Complex Obligation (BEST)

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

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

Innermost TRS:
Rules:
F(0', 1', z0) -> c(F(g(z0), g(z0), z0))
F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
f(0', 1', z0) -> f(g(z0), g(z0), z0)
f(g(z0), z1, z2) -> g(f(z0, z1, z2))
f(z0, g(z1), z2) -> g(f(z0, z1, z2))
f(z0, z1, g(z2)) -> g(f(z0, z1, z2))

Types:
F :: 0':1':g -> 0':1':g -> 0':1':g -> c:c1:c2:c3
0' :: 0':1':g
1' :: 0':1':g
c :: c:c1:c2:c3 -> c:c1:c2:c3
g :: 0':1':g -> 0':1':g
c1 :: c:c1:c2:c3 -> c:c1:c2:c3
c2 :: c:c1:c2:c3 -> c:c1:c2:c3
c3 :: c:c1:c2:c3 -> c:c1:c2:c3
f :: 0':1':g -> 0':1':g -> 0':1':g -> 0':1':g
hole_c:c1:c2:c31_4 :: c:c1:c2:c3
hole_0':1':g2_4 :: 0':1':g
gen_c:c1:c2:c33_4 :: Nat -> c:c1:c2:c3
gen_0':1':g4_4 :: Nat -> 0':1':g


Generator Equations:
gen_c:c1:c2:c33_4(0) <=> hole_c:c1:c2:c31_4
gen_c:c1:c2:c33_4(+(x, 1)) <=> c(gen_c:c1:c2:c33_4(x))
gen_0':1':g4_4(0) <=> 1'
gen_0':1':g4_4(+(x, 1)) <=> g(gen_0':1':g4_4(x))


The following defined symbols remain to be analysed:
F, f
----------------------------------------

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

(19)
BOUNDS(n^1, INF)

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

(20)
Obligation:
Innermost TRS:
Rules:
F(0', 1', z0) -> c(F(g(z0), g(z0), z0))
F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
f(0', 1', z0) -> f(g(z0), g(z0), z0)
f(g(z0), z1, z2) -> g(f(z0, z1, z2))
f(z0, g(z1), z2) -> g(f(z0, z1, z2))
f(z0, z1, g(z2)) -> g(f(z0, z1, z2))

Types:
F :: 0':1':g -> 0':1':g -> 0':1':g -> c:c1:c2:c3
0' :: 0':1':g
1' :: 0':1':g
c :: c:c1:c2:c3 -> c:c1:c2:c3
g :: 0':1':g -> 0':1':g
c1 :: c:c1:c2:c3 -> c:c1:c2:c3
c2 :: c:c1:c2:c3 -> c:c1:c2:c3
c3 :: c:c1:c2:c3 -> c:c1:c2:c3
f :: 0':1':g -> 0':1':g -> 0':1':g -> 0':1':g
hole_c:c1:c2:c31_4 :: c:c1:c2:c3
hole_0':1':g2_4 :: 0':1':g
gen_c:c1:c2:c33_4 :: Nat -> c:c1:c2:c3
gen_0':1':g4_4 :: Nat -> 0':1':g


Lemmas:
F(gen_0':1':g4_4(+(1, n6_4)), gen_0':1':g4_4(b), gen_0':1':g4_4(c)) -> *5_4, rt in Omega(n6_4)


Generator Equations:
gen_c:c1:c2:c33_4(0) <=> hole_c:c1:c2:c31_4
gen_c:c1:c2:c33_4(+(x, 1)) <=> c(gen_c:c1:c2:c33_4(x))
gen_0':1':g4_4(0) <=> 1'
gen_0':1':g4_4(+(x, 1)) <=> g(gen_0':1':g4_4(x))


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

(21) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
f(gen_0':1':g4_4(+(1, n2072_4)), gen_0':1':g4_4(b), gen_0':1':g4_4(c)) -> *5_4, rt in Omega(0)

Induction Base:
f(gen_0':1':g4_4(+(1, 0)), gen_0':1':g4_4(b), gen_0':1':g4_4(c))

Induction Step:
f(gen_0':1':g4_4(+(1, +(n2072_4, 1))), gen_0':1':g4_4(b), gen_0':1':g4_4(c)) ->_R^Omega(0)
g(f(gen_0':1':g4_4(+(1, n2072_4)), gen_0':1':g4_4(b), gen_0':1':g4_4(c))) ->_IH
g(*5_4)

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

(22)
BOUNDS(1, INF)

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

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

(24)
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:

   f(0, 1, x) -> f(g(x), g(x), x) [1]
   f(g(x), y, z) -> g(f(x, y, z)) [1]
   f(x, g(y), z) -> g(f(x, y, z)) [1]
   f(x, y, g(z)) -> g(f(x, y, z)) [1]

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

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

(26)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(0, 1, x) -> f(g(x), g(x), x) [1]
   f(g(x), y, z) -> g(f(x, y, z)) [1]
   f(x, g(y), z) -> g(f(x, y, z)) [1]
   f(x, y, g(z)) -> g(f(x, y, z)) [1]

The TRS has the following type information:
f :: 0:1:g -> 0:1:g -> 0:1:g -> 0:1:g
0 :: 0:1:g
1 :: 0:1:g
g :: 0:1:g -> 0:1:g

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

(27) 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:

   f_3

(c) The following functions are completely defined:
none

Due to the following rules being added:
none

And the following fresh constants: none

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

(28)
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:

   f(0, 1, x) -> f(g(x), g(x), x) [1]
   f(g(x), y, z) -> g(f(x, y, z)) [1]
   f(x, g(y), z) -> g(f(x, y, z)) [1]
   f(x, y, g(z)) -> g(f(x, y, z)) [1]

The TRS has the following type information:
f :: 0:1:g -> 0:1:g -> 0:1:g -> 0:1:g
0 :: 0:1:g
1 :: 0:1:g
g :: 0:1:g -> 0:1:g

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

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

(30)
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:

   f(0, 1, x) -> f(g(x), g(x), x) [1]
   f(g(x), y, z) -> g(f(x, y, z)) [1]
   f(x, g(y), z) -> g(f(x, y, z)) [1]
   f(x, y, g(z)) -> g(f(x, y, z)) [1]

The TRS has the following type information:
f :: 0:1:g -> 0:1:g -> 0:1:g -> 0:1:g
0 :: 0:1:g
1 :: 0:1:g
g :: 0:1:g -> 0:1:g

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

(31) 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
   1 => 1

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

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

   f(z', z'', z1) -{ 1 }-> f(1 + x, 1 + x, x) :|: x >= 0, z'' = 1, z1 = x, z' = 0
   f(z', z'', z1) -{ 1 }-> 1 + f(x, y, z) :|: z' = 1 + x, z1 = z, z >= 0, z'' = y, x >= 0, y >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(x, y, z) :|: z1 = z, z >= 0, z' = x, x >= 0, y >= 0, z'' = 1 + y
   f(z', z'', z1) -{ 1 }-> 1 + f(x, y, z) :|: z >= 0, z' = x, z'' = y, x >= 0, y >= 0, z1 = 1 + z


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

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

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

   f(z', z'', z1) -{ 1 }-> f(1 + z1, 1 + z1, z1) :|: z1 >= 0, z'' = 1, z' = 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'', z1 - 1) :|: z1 - 1 >= 0, z' >= 0, z'' >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'' - 1, z1) :|: z1 >= 0, z' >= 0, z'' - 1 >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z' - 1, z'', z1) :|: z1 >= 0, z' - 1 >= 0, z'' >= 0


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

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

   { f }

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

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

   f(z', z'', z1) -{ 1 }-> f(1 + z1, 1 + z1, z1) :|: z1 >= 0, z'' = 1, z' = 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'', z1 - 1) :|: z1 - 1 >= 0, z' >= 0, z'' >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'' - 1, z1) :|: z1 >= 0, z' >= 0, z'' - 1 >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z' - 1, z'', z1) :|: z1 >= 0, z' - 1 >= 0, z'' >= 0

Function symbols to be analyzed: {f}

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

(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', z'', z1) -{ 1 }-> f(1 + z1, 1 + z1, z1) :|: z1 >= 0, z'' = 1, z' = 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'', z1 - 1) :|: z1 - 1 >= 0, z' >= 0, z'' >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'' - 1, z1) :|: z1 >= 0, z' >= 0, z'' - 1 >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z' - 1, z'', z1) :|: z1 >= 0, z' - 1 >= 0, z'' >= 0

Function symbols to be analyzed: {f}

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

(39) 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

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

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

   f(z', z'', z1) -{ 1 }-> f(1 + z1, 1 + z1, z1) :|: z1 >= 0, z'' = 1, z' = 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'', z1 - 1) :|: z1 - 1 >= 0, z' >= 0, z'' >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'' - 1, z1) :|: z1 >= 0, z' >= 0, z'' - 1 >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z' - 1, z'', z1) :|: z1 >= 0, z' - 1 >= 0, z'' >= 0

Function symbols to be analyzed: {f}
Previous analysis results are:
  f: runtime: ?, size: O(1) [0]

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

(41) 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: ?

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

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

   f(z', z'', z1) -{ 1 }-> f(1 + z1, 1 + z1, z1) :|: z1 >= 0, z'' = 1, z' = 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'', z1 - 1) :|: z1 - 1 >= 0, z' >= 0, z'' >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z', z'' - 1, z1) :|: z1 >= 0, z' >= 0, z'' - 1 >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(z' - 1, z'', z1) :|: z1 >= 0, z' - 1 >= 0, z'' >= 0

Function symbols to be analyzed: {f}
Previous analysis results are:
  f: runtime: INF, size: O(1) [0]

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

(43) 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:

   f(v0, v1, v2) -> null_f [0]

And the following fresh constants:    null_f

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

(44)
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:

   f(0, 1, x) -> f(g(x), g(x), x) [1]
   f(g(x), y, z) -> g(f(x, y, z)) [1]
   f(x, g(y), z) -> g(f(x, y, z)) [1]
   f(x, y, g(z)) -> g(f(x, y, z)) [1]
   f(v0, v1, v2) -> null_f [0]

The TRS has the following type information:
f :: 0:1:g:null_f -> 0:1:g:null_f -> 0:1:g:null_f -> 0:1:g:null_f
0 :: 0:1:g:null_f
1 :: 0:1:g:null_f
g :: 0:1:g:null_f -> 0:1:g:null_f
null_f :: 0:1:g:null_f

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

(45) 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
   1 => 1
   null_f => 0

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

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

   f(z', z'', z1) -{ 1 }-> f(1 + x, 1 + x, x) :|: x >= 0, z'' = 1, z1 = x, z' = 0
   f(z', z'', z1) -{ 0 }-> 0 :|: v0 >= 0, z1 = v2, v1 >= 0, z'' = v1, v2 >= 0, z' = v0
   f(z', z'', z1) -{ 1 }-> 1 + f(x, y, z) :|: z' = 1 + x, z1 = z, z >= 0, z'' = y, x >= 0, y >= 0
   f(z', z'', z1) -{ 1 }-> 1 + f(x, y, z) :|: z1 = z, z >= 0, z' = x, x >= 0, y >= 0, z'' = 1 + y
   f(z', z'', z1) -{ 1 }-> 1 + f(x, y, z) :|: z >= 0, z' = x, z'' = y, x >= 0, y >= 0, z1 = 1 + z

Only complete derivations are relevant for the runtime complexity.

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

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0, 1, z0) -> f(g(z0), g(z0), z0)
   f(g(z0), z1, z2) -> g(f(z0, z1, z2))
   f(z0, g(z1), z2) -> g(f(z0, z1, z2))
   f(z0, z1, g(z2)) -> g(f(z0, z1, z2))
Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
S tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
K tuples:none
Defined Rule Symbols:   f_3

Defined Pair Symbols:   F_3

Compound Symbols:   c_1, c1_1, c2_1, c3_1


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

(49) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   f(0, 1, z0) -> f(g(z0), g(z0), z0)
   f(g(z0), z1, z2) -> g(f(z0, z1, z2))
   f(z0, g(z1), z2) -> g(f(z0, z1, z2))
   f(z0, z1, g(z2)) -> g(f(z0, z1, z2))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
S tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c_1, c1_1, c2_1, c3_1


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

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

(52)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))

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

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

(54)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))

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

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

(56)
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:

   F(0, 1, z0) -> c(F(g(z0), g(z0), z0)) [1]
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2)) [1]
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2)) [1]
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2)) [1]

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

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

(58)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   F(0, 1, z0) -> c(F(g(z0), g(z0), z0)) [1]
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2)) [1]
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2)) [1]
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2)) [1]

The TRS has the following type information:
F :: 0:1:g -> 0:1:g -> 0:1:g -> c:c1:c2:c3
0 :: 0:1:g
1 :: 0:1:g
c :: c:c1:c2:c3 -> c:c1:c2:c3
g :: 0:1:g -> 0:1:g
c1 :: c:c1:c2:c3 -> c:c1:c2:c3
c2 :: c:c1:c2:c3 -> c:c1:c2:c3
c3 :: c:c1:c2:c3 -> c:c1:c2:c3

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

(59) 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:

   F_3

(c) The following functions are completely defined:
none

Due to the following rules being added:
none

And the following fresh constants:    const

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

(60)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   F(0, 1, z0) -> c(F(g(z0), g(z0), z0)) [1]
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2)) [1]
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2)) [1]
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2)) [1]

The TRS has the following type information:
F :: 0:1:g -> 0:1:g -> 0:1:g -> c:c1:c2:c3
0 :: 0:1:g
1 :: 0:1:g
c :: c:c1:c2:c3 -> c:c1:c2:c3
g :: 0:1:g -> 0:1:g
c1 :: c:c1:c2:c3 -> c:c1:c2:c3
c2 :: c:c1:c2:c3 -> c:c1:c2:c3
c3 :: c:c1:c2:c3 -> c:c1:c2:c3
const :: c:c1:c2:c3

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

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

(62)
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:

   F(0, 1, z0) -> c(F(g(z0), g(z0), z0)) [1]
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2)) [1]
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2)) [1]
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2)) [1]

The TRS has the following type information:
F :: 0:1:g -> 0:1:g -> 0:1:g -> c:c1:c2:c3
0 :: 0:1:g
1 :: 0:1:g
c :: c:c1:c2:c3 -> c:c1:c2:c3
g :: 0:1:g -> 0:1:g
c1 :: c:c1:c2:c3 -> c:c1:c2:c3
c2 :: c:c1:c2:c3 -> c:c1:c2:c3
c3 :: c:c1:c2:c3 -> c:c1:c2:c3
const :: c:c1:c2:c3

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

(63) 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
   1 => 1
   const => 0

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

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

   F(z, z', z'') -{ 1 }-> 1 + F(z0, z1, z2) :|: z'' = z2, z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0, z2 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z0, z1, z2) :|: z'' = z2, z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1, z2 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z0, z1, z2) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0, z'' = 1 + z2, z2 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(1 + z0, 1 + z0, z0) :|: z'' = z0, z0 >= 0, z' = 1, z = 0


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

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

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

   F(z, z', z'') -{ 1 }-> 1 + F(z, z', z'' - 1) :|: z' >= 0, z >= 0, z'' - 1 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z, z' - 1, z'') :|: z' - 1 >= 0, z >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z - 1, z', z'') :|: z' >= 0, z - 1 >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(1 + z'', 1 + z'', z'') :|: z'' >= 0, z' = 1, z = 0


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

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

   { F }

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

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

   F(z, z', z'') -{ 1 }-> 1 + F(z, z', z'' - 1) :|: z' >= 0, z >= 0, z'' - 1 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z, z' - 1, z'') :|: z' - 1 >= 0, z >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z - 1, z', z'') :|: z' >= 0, z - 1 >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(1 + z'', 1 + z'', z'') :|: z'' >= 0, z' = 1, z = 0

Function symbols to be analyzed: {F}

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

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

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

   F(z, z', z'') -{ 1 }-> 1 + F(z, z', z'' - 1) :|: z' >= 0, z >= 0, z'' - 1 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z, z' - 1, z'') :|: z' - 1 >= 0, z >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z - 1, z', z'') :|: z' >= 0, z - 1 >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(1 + z'', 1 + z'', z'') :|: z'' >= 0, z' = 1, z = 0

Function symbols to be analyzed: {F}

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

(71) 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

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

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

   F(z, z', z'') -{ 1 }-> 1 + F(z, z', z'' - 1) :|: z' >= 0, z >= 0, z'' - 1 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z, z' - 1, z'') :|: z' - 1 >= 0, z >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z - 1, z', z'') :|: z' >= 0, z - 1 >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(1 + z'', 1 + z'', z'') :|: z'' >= 0, z' = 1, z = 0

Function symbols to be analyzed: {F}
Previous analysis results are:
  F: runtime: ?, size: O(1) [0]

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

(73) 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: ?

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

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

   F(z, z', z'') -{ 1 }-> 1 + F(z, z', z'' - 1) :|: z' >= 0, z >= 0, z'' - 1 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z, z' - 1, z'') :|: z' - 1 >= 0, z >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z - 1, z', z'') :|: z' >= 0, z - 1 >= 0, z'' >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(1 + z'', 1 + z'', z'') :|: z'' >= 0, z' = 1, z = 0

Function symbols to be analyzed: {F}
Previous analysis results are:
  F: runtime: INF, size: O(1) [0]

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

(75) 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:

   F(v0, v1, v2) -> null_F [0]

And the following fresh constants:    null_F

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

(76)
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:

   F(0, 1, z0) -> c(F(g(z0), g(z0), z0)) [1]
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2)) [1]
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2)) [1]
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2)) [1]
   F(v0, v1, v2) -> null_F [0]

The TRS has the following type information:
F :: 0:1:g -> 0:1:g -> 0:1:g -> c:c1:c2:c3:null_F
0 :: 0:1:g
1 :: 0:1:g
c :: c:c1:c2:c3:null_F -> c:c1:c2:c3:null_F
g :: 0:1:g -> 0:1:g
c1 :: c:c1:c2:c3:null_F -> c:c1:c2:c3:null_F
c2 :: c:c1:c2:c3:null_F -> c:c1:c2:c3:null_F
c3 :: c:c1:c2:c3:null_F -> c:c1:c2:c3:null_F
null_F :: c:c1:c2:c3:null_F

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

(77) 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
   1 => 1
   null_F => 0

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

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

   F(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z0, z1, z2) :|: z'' = z2, z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0, z2 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z0, z1, z2) :|: z'' = z2, z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1, z2 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(z0, z1, z2) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0, z'' = 1 + z2, z2 >= 0
   F(z, z', z'') -{ 1 }-> 1 + F(1 + z0, 1 + z0, z0) :|: z'' = z0, z0 >= 0, z' = 1, z = 0

Only complete derivations are relevant for the runtime complexity.

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

(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(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(1) = 0
   POL(F(x_1, x_2, x_3)) = x_3
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c2(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(g(x_1)) = [1] + x_1

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
S tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(z0), z1, z2) -> c1(F(z0, z1, z2))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
K tuples:
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c_1, c1_1, c2_1, c3_1


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

(81) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(z0), z1, z2) -> c1(F(z0, z1, z2)) by 
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(g(y0)), z1, z2) -> c1(F(g(y0), z1, z2))
   F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(g(y0)), z1, z2) -> c1(F(g(y0), z1, z2))
   F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
S tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(z0, g(z1), z2) -> c2(F(z0, z1, z2))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(g(y0)), z1, z2) -> c1(F(g(y0), z1, z2))
   F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
K tuples:
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c_1, c2_1, c3_1, c1_1


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

(83) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, g(z1), z2) -> c2(F(z0, z1, z2)) by 
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(g(y0)), z1, z2) -> c1(F(g(y0), z1, z2))
   F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
S tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(g(y0)), z1, z2) -> c1(F(g(y0), z1, z2))
   F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
K tuples:
   F(z0, z1, g(z2)) -> c3(F(z0, z1, z2))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c_1, c3_1, c1_1, c2_1


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

(85) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, z1, g(z2)) -> c3(F(z0, z1, z2)) by 
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(g(y0)), z1, z2) -> c1(F(g(y0), z1, z2))
   F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
S tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(g(y0)), z1, z2) -> c1(F(g(y0), z1, z2))
   F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c_1, c1_1, c2_1, c3_1


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

(87) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(g(y0)), z1, z2) -> c1(F(g(y0), z1, z2)) by 
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
S tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c_1, c1_1, c2_1, c3_1


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

(89) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(z0), g(y1), z2) -> c1(F(z0, g(y1), z2)) by 
   F(g(g(y0)), g(z1), z2) -> c1(F(g(y0), g(z1), z2))
   F(g(g(y0)), g(z1), g(y2)) -> c1(F(g(y0), g(z1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(z1), z2) -> c1(F(g(g(y0)), g(z1), z2))
   F(g(g(y0)), g(g(y1)), z2) -> c1(F(g(y0), g(g(y1)), z2))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(g(g(y0))), g(z1), g(y2)) -> c1(F(g(g(y0)), g(z1), g(y2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c1(F(g(y0), g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(y0)), g(g(y1)), g(y2)) -> c1(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
S tuples:
   F(0, 1, z0) -> c(F(g(z0), g(z0), z0))
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c_1, c1_1, c2_1, c3_1


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

(91) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(0, 1, z0) -> c(F(g(z0), g(z0), z0)) by 
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
S tuples:
   F(g(0), 1, z2) -> c1(F(0, 1, z2))
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c1_1, c2_1, c3_1, c_1


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

(93) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(0), 1, z2) -> c1(F(0, 1, z2)) by 
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
S tuples:
   F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2)))
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c1_1, c2_1, c3_1, c_1


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

(95) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(z0), z1, g(y2)) -> c1(F(z0, z1, g(y2))) by 
   F(g(g(y0)), z1, g(z2)) -> c1(F(g(y0), z1, g(z2)))
   F(g(0), g(1), g(z2)) -> c1(F(0, g(1), g(z2)))
   F(g(z0), g(g(y1)), g(z2)) -> c1(F(z0, g(g(y1)), g(z2)))
   F(g(z0), g(y1), g(z2)) -> c1(F(z0, g(y1), g(z2)))
   F(g(g(0)), g(1), g(z2)) -> c1(F(g(0), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(z2)) -> c1(F(g(g(y0)), g(y1), g(z2)))
   F(g(g(y0)), g(g(y1)), g(z2)) -> c1(F(g(y0), g(g(y1)), g(z2)))
   F(g(g(y0)), g(y1), g(z2)) -> c1(F(g(y0), g(y1), g(z2)))
   F(g(0), 1, g(z2)) -> c1(F(0, 1, g(z2)))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(0)), 1, g(z2)) -> c1(F(g(0), 1, g(z2)))
   F(g(g(g(y0))), z1, g(z2)) -> c1(F(g(g(y0)), z1, g(z2)))
   F(g(g(y0)), z1, g(g(y2))) -> c1(F(g(y0), z1, g(g(y2))))
   F(g(z0), g(y1), g(g(y2))) -> c1(F(z0, g(y1), g(g(y2))))
   F(g(g(y0)), g(y1), g(g(y2))) -> c1(F(g(y0), g(y1), g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c1(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(z2)) -> c1(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c1(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(y0))), g(y1), g(g(y2))) -> c1(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(y0))) -> c1(F(0, 1, g(g(y0))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
S tuples:
   F(0, g(1), z2) -> c2(F(0, 1, z2))
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c2_1, c3_1, c1_1, c_1


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

(97) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(0, g(1), z2) -> c2(F(0, 1, z2)) by 
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
S tuples:
   F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2))
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c2_1, c3_1, c1_1, c_1


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

(99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, g(g(y1)), z2) -> c2(F(z0, g(y1), z2)) by 
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
S tuples:
   F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2)))
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c2_1, c3_1, c1_1, c_1


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

(101) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, g(z1), g(y2)) -> c2(F(z0, z1, g(y2))) by 
   F(z0, g(g(y1)), g(z2)) -> c2(F(z0, g(y1), g(z2)))
   F(g(0), g(g(1)), g(z2)) -> c2(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(g(y1)), g(z2)) -> c2(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(g(y1))), g(z2)) -> c2(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(g(y1)), g(z2)) -> c2(F(g(y0), g(y1), g(z2)))
   F(0, g(1), g(z2)) -> c2(F(0, 1, g(z2)))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(0, g(g(1)), g(z2)) -> c2(F(0, g(1), g(z2)))
   F(z0, g(g(g(y1))), g(z2)) -> c2(F(z0, g(g(y1)), g(z2)))
   F(z0, g(g(y1)), g(g(y2))) -> c2(F(z0, g(y1), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(y2))) -> c2(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(z2)) -> c2(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(g(1)), g(z2)) -> c2(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c2(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(g(y1)), g(g(y2))) -> c2(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c2(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c2(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(0, g(1), g(g(y0))) -> c2(F(0, 1, g(g(y0))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(z2)) -> c2(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
S tuples:
   F(g(0), g(1), z2) -> c2(F(g(0), 1, z2))
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c2_1, c3_1, c1_1, c_1


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

(103) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(0), g(1), z2) -> c2(F(g(0), 1, z2)) by 
   F(g(0), g(1), g(g(y2))) -> c2(F(g(0), 1, g(g(y2))))
   F(g(0), g(1), g(y0)) -> c2(F(g(0), 1, g(y0)))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
S tuples:
   F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2))
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c2_1, c3_1, c1_1, c_1


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

(105) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(g(y0)), g(z1), z2) -> c2(F(g(g(y0)), z1, z2)) by 
   F(g(g(z0)), g(g(y1)), z2) -> c2(F(g(g(z0)), g(y1), z2))
   F(g(g(z0)), g(g(g(y1))), z2) -> c2(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c2(F(g(g(z0)), g(y1), g(y2)))
   F(g(g(z0)), g(z1), g(g(y2))) -> c2(F(g(g(z0)), z1, g(g(y2))))
   F(g(g(z0)), g(z1), g(y2)) -> c2(F(g(g(z0)), z1, g(y2)))
   F(g(g(z0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(z0)), g(g(y1)), g(y2)))
   F(g(g(z0)), g(g(y1)), g(g(y2))) -> c2(F(g(g(z0)), g(y1), g(g(y2))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c2(F(g(g(g(y0))), g(y1), z2))
   F(g(g(0)), g(1), g(y0)) -> c2(F(g(g(0)), 1, g(y0)))
   F(g(g(g(y0))), g(z1), g(y2)) -> c2(F(g(g(g(y0))), z1, g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c2(F(g(g(g(y0))), g(y1), g(y2)))
   F(g(g(g(g(y0)))), g(g(y1)), z2) -> c2(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(y1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(y1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(y1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(0))), g(1), g(y0)) -> c2(F(g(g(g(0))), 1, g(y0)))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c2(F(g(g(g(g(y0)))), z1, g(y2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(y1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(z0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(z0)), g(g(y1)), g(g(y2))))
   F(g(g(z0)), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(z0)), g(g(g(y1))), g(y2)))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(0)), g(g(g(1))), g(y0)) -> c2(F(g(g(0)), g(g(1)), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(y2)))
   F(g(g(g(0))), g(g(g(1))), g(y0)) -> c2(F(g(g(g(0))), g(g(1)), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
S tuples:
   F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2))
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c2_1, c3_1, c1_1, c_1


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

(107) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(y0), g(g(y1)), z2) -> c2(F(g(y0), g(y1), z2)) by 
   F(g(z0), g(g(g(y1))), z2) -> c2(F(g(z0), g(g(y1)), z2))
   F(g(z0), g(g(z1)), g(y2)) -> c2(F(g(z0), g(z1), g(y2)))
   F(g(z0), g(g(z1)), g(g(y2))) -> c2(F(g(z0), g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(z0), g(g(g(y1))), g(y2)) -> c2(F(g(z0), g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(y1))), g(g(y2))) -> c2(F(g(z0), g(g(y1)), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), g(y2)) -> c2(F(g(z0), g(g(g(y1))), g(y2)))
   F(g(0), g(g(g(1))), g(y0)) -> c2(F(g(0), g(g(1)), g(y0)))
   F(g(g(y0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(y0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(y0)), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(y2)))
   F(g(g(0)), g(g(g(1))), g(y0)) -> c2(F(g(g(0)), g(g(1)), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(y2)))
   F(g(g(g(0))), g(g(g(1))), g(y0)) -> c2(F(g(g(g(0))), g(g(1)), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
S tuples:
   F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c2_1, c3_1, c1_1, c_1


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

(109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(y0), g(z1), g(y2)) -> c2(F(g(y0), z1, g(y2))) by 
   F(g(z0), g(g(y1)), g(z2)) -> c2(F(g(z0), g(y1), g(z2)))
   F(g(z0), g(z1), g(g(y2))) -> c2(F(g(z0), z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(z0), g(g(g(y1))), g(z2)) -> c2(F(g(z0), g(g(y1)), g(z2)))
   F(g(z0), g(g(y1)), g(g(y2))) -> c2(F(g(z0), g(y1), g(g(y2))))
   F(g(0), g(g(1)), g(z2)) -> c2(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(g(y1)), g(z2)) -> c2(F(g(g(y0)), g(y1), g(z2)))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(z2)) -> c2(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(g(1)), g(z2)) -> c2(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c2(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(g(y1)), g(g(y2))) -> c2(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c2(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c2(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(z2)) -> c2(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(z0), g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(z0), g(g(g(y1))), g(g(y2))) -> c2(F(g(z0), g(g(y1)), g(g(y2))))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(z2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(z2)) -> c2(F(g(0), g(g(g(1))), g(z2)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c2(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(0, 1, g(z2)) -> c3(F(0, 1, z2))
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1


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

(111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(0, 1, g(z2)) -> c3(F(0, 1, z2)) by 
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2)))
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1


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

(113) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, z1, g(g(y2))) -> c3(F(z0, z1, g(y2))) by 
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(y1), g(g(z2))) -> c3(F(g(y0), g(y1), g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(0, 1, g(g(z2))) -> c3(F(0, 1, g(z2)))
   F(0, 1, g(g(g(y0)))) -> c3(F(0, 1, g(g(y0))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2))
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1


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

(115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(0), 1, g(z2)) -> c3(F(g(0), 1, z2)) by 
   F(g(0), 1, g(g(y0))) -> c3(F(g(0), 1, g(y0)))
   F(g(0), 1, g(g(g(y2)))) -> c3(F(g(0), 1, g(g(y2))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2))
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1


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

(117) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(g(y0)), z1, g(z2)) -> c3(F(g(g(y0)), z1, z2)) by 
   F(g(g(z0)), z1, g(g(y2))) -> c3(F(g(g(z0)), z1, g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c3(F(g(g(z0)), g(y1), g(y2)))
   F(g(g(z0)), z1, g(g(g(y2)))) -> c3(F(g(g(z0)), z1, g(g(y2))))
   F(g(g(z0)), g(g(y1)), g(g(y2))) -> c3(F(g(g(z0)), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(z0)), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(y1), g(z2)) -> c3(F(g(g(z0)), g(y1), z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(0)), 1, g(g(y0))) -> c3(F(g(g(0)), 1, g(y0)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c3(F(g(g(g(y0))), z1, g(y2)))
   F(g(g(0)), g(1), g(g(y0))) -> c3(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(g(y2))) -> c3(F(g(g(g(y0))), g(y1), g(y2)))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(g(y0))) -> c3(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(0))), 1, g(g(y0))) -> c3(F(g(g(g(0))), 1, g(y0)))
   F(g(g(g(g(y0)))), z1, g(g(y2))) -> c3(F(g(g(g(g(y0)))), z1, g(y2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(y2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(1), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(z0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(y1)), g(g(y2))))
   F(g(g(z0)), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(z0)), g(g(g(y1))), g(y2)))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c3(F(g(g(0)), g(g(1)), g(y0)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(y2)))
   F(g(g(g(0))), g(g(1)), g(g(y0))) -> c3(F(g(g(g(0))), g(g(1)), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(y0)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(1))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(y2)))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2))
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1


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

(119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(y0), g(y1), g(z2)) -> c3(F(g(y0), g(y1), z2)) by 
   F(g(z0), g(z1), g(g(y2))) -> c3(F(g(z0), g(z1), g(y2)))
   F(g(z0), g(z1), g(g(g(y2)))) -> c3(F(g(z0), g(z1), g(g(y2))))
   F(g(z0), g(g(y1)), g(g(y2))) -> c3(F(g(z0), g(g(y1)), g(y2)))
   F(g(0), g(1), g(g(y0))) -> c3(F(g(0), g(1), g(y0)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c3(F(g(g(y0)), g(z1), g(y2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c3(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(z1), g(z2)) -> c3(F(g(g(y0)), g(z1), z2))
   F(g(g(y0)), g(g(y1)), g(z2)) -> c3(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(z1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c3(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(y1)), g(g(y2))) -> c3(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(1), g(g(y0))) -> c3(F(g(g(0)), g(1), g(y0)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(z0), g(g(y1)), g(z2)) -> c3(F(g(z0), g(g(y1)), z2))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(g(y0))) -> c3(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(z1), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(1), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(z1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(z0), g(g(y1)), g(g(y2))))
   F(g(z0), g(g(g(y1))), g(g(y2))) -> c3(F(g(z0), g(g(g(y1))), g(y2)))
   F(g(0), g(g(1)), g(g(y0))) -> c3(F(g(0), g(g(1)), g(y0)))
   F(g(g(y0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(y0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(y2)))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c3(F(g(g(0)), g(g(1)), g(y0)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(y2)))
   F(g(g(g(0))), g(g(1)), g(g(y0))) -> c3(F(g(g(g(0))), g(g(1)), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(y0)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(1))), g(g(y0))) -> c3(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(1))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(0), g(g(g(g(1)))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(0), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(0), g(g(g(g(g(1))))), g(y0)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(z1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2)))
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1


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

(121) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(g(y0), z1, g(g(y2))) -> c3(F(g(y0), z1, g(y2))) by 
   F(g(z0), z1, g(g(g(y2)))) -> c3(F(g(z0), z1, g(g(y2))))
   F(g(z0), g(g(y1)), g(g(z2))) -> c3(F(g(z0), g(g(y1)), g(z2)))
   F(g(z0), g(y1), g(g(g(y2)))) -> c3(F(g(z0), g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(z0), g(y1), g(g(z2))) -> c3(F(g(z0), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(g(z0), g(g(g(y1))), g(g(z2))) -> c3(F(g(z0), g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(z0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(z0), g(g(y1)), g(g(y2))))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(z0), g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(z0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(z0), z1, g(g(g(g(y2))))) -> c3(F(g(z0), z1, g(g(g(y2)))))
   F(g(z0), g(y1), g(g(g(g(y2))))) -> c3(F(g(z0), g(y1), g(g(g(y2)))))
   F(g(g(y0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(y0)), z1, g(g(g(y2)))))
   F(g(g(y0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(0), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), z1, g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(0))), 1, g(g(g(g(y0))))) -> c3(F(g(g(g(0))), 1, g(g(g(y0)))))
   F(g(g(g(g(y0)))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), z1, g(g(g(y2)))))
   F(g(g(g(y0))), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), z1, g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))))
   F(g(g(0)), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(z0), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(y1), g(g(g(g(y2))))))
   F(g(z0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(z0), z1, g(g(g(g(y2))))) -> c3(F(g(z0), z1, g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(0), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), z1, g(g(g(g(y2))))))
   F(g(g(g(0))), 1, g(g(g(g(y0))))) -> c3(F(g(g(g(0))), 1, g(g(g(y0)))))
   F(g(g(g(g(y0)))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), z1, g(g(g(y2)))))
   F(g(g(g(y0))), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), z1, g(g(g(g(y2))))))
   F(g(g(0)), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), 1, g(g(g(g(g(y0)))))))
   F(g(z0), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(y1), g(g(g(g(y2))))))
   F(g(z0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(0, g(1), g(z2)) -> c3(F(0, g(1), z2))
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(z0), z1, g(g(g(g(y2))))) -> c3(F(g(z0), z1, g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(0), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), z1, g(g(g(g(y2))))))
   F(g(g(g(0))), 1, g(g(g(g(y0))))) -> c3(F(g(g(g(0))), 1, g(g(g(y0)))))
   F(g(g(g(g(y0)))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), z1, g(g(g(y2)))))
   F(g(g(g(y0))), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), z1, g(g(g(g(y2))))))
   F(g(g(0)), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), 1, g(g(g(g(g(y0)))))))
   F(g(z0), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(y1), g(g(g(g(y2))))))
   F(g(z0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1


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

(123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(0, g(1), g(z2)) -> c3(F(0, g(1), z2)) by 
   F(0, g(1), g(g(y0))) -> c3(F(0, g(1), g(y0)))
   F(0, g(1), g(g(g(y2)))) -> c3(F(0, g(1), g(g(y2))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(0, g(1), g(g(g(g(g(y0)))))) -> c3(F(0, g(1), g(g(g(g(y0))))))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(z0), z1, g(g(g(g(y2))))) -> c3(F(g(z0), z1, g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(0), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), z1, g(g(g(g(y2))))))
   F(g(g(g(0))), 1, g(g(g(g(y0))))) -> c3(F(g(g(g(0))), 1, g(g(g(y0)))))
   F(g(g(g(g(y0)))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), z1, g(g(g(y2)))))
   F(g(g(g(y0))), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), z1, g(g(g(g(y2))))))
   F(g(g(0)), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), 1, g(g(g(g(g(y0)))))))
   F(g(z0), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(y1), g(g(g(g(y2))))))
   F(g(z0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(0, g(1), g(g(g(g(g(y0)))))) -> c3(F(0, g(1), g(g(g(g(y0))))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2))
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(z0), z1, g(g(g(g(y2))))) -> c3(F(g(z0), z1, g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(0), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), z1, g(g(g(g(y2))))))
   F(g(g(g(0))), 1, g(g(g(g(y0))))) -> c3(F(g(g(g(0))), 1, g(g(g(y0)))))
   F(g(g(g(g(y0)))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), z1, g(g(g(y2)))))
   F(g(g(g(y0))), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), z1, g(g(g(g(y2))))))
   F(g(g(0)), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), 1, g(g(g(g(g(y0)))))))
   F(g(z0), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(y1), g(g(g(g(y2))))))
   F(g(z0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(0, g(1), g(g(g(g(g(y0)))))) -> c3(F(0, g(1), g(g(g(g(y0))))))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1


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

(125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, g(g(y1)), g(z2)) -> c3(F(z0, g(g(y1)), z2)) by 
   F(z0, g(g(z1)), g(g(y2))) -> c3(F(z0, g(g(z1)), g(y2)))
   F(z0, g(g(z1)), g(g(g(y2)))) -> c3(F(z0, g(g(z1)), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c3(F(g(g(y0)), g(g(z1)), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c3(F(g(y0), g(g(z1)), g(y2)))
   F(g(y0), g(g(z1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(z1)), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(z1)), z2))
   F(g(g(y0)), g(g(z1)), g(z2)) -> c3(F(g(g(y0)), g(g(z1)), z2))
   F(g(g(y0)), g(g(z1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(z1)), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(z1)), g(y2)))
   F(g(y0), g(g(z1)), g(z2)) -> c3(F(g(y0), g(g(z1)), z2))
   F(g(g(g(g(y0)))), g(g(z1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(z1)), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(z1)), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(y2)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))))
   F(z0, g(g(g(y1))), g(z2)) -> c3(F(z0, g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(y0), g(g(g(y1))), g(z2)) -> c3(F(g(y0), g(g(g(y1))), z2))
   F(0, g(g(1)), g(g(y0))) -> c3(F(0, g(g(1)), g(y0)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c3(F(z0, g(g(g(y1))), g(y2)))
   F(g(0), g(g(1)), g(g(y0))) -> c3(F(g(0), g(g(1)), g(y0)))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c3(F(g(y0), g(g(g(y1))), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(y0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(y2)))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c3(F(g(g(0)), g(g(1)), g(y0)))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(y2)))
   F(g(g(g(0))), g(g(1)), g(g(y0))) -> c3(F(g(g(g(0))), g(g(1)), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(y0)))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(y2))) -> c3(F(z0, g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(1))), g(g(y0))) -> c3(F(g(0), g(g(g(1))), g(y0)))
   F(g(y0), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(y2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c3(F(0, g(g(g(1))), g(y0)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(1))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(y0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(g(y0))) -> c3(F(g(0), g(g(g(g(1)))), g(y0)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(0), g(g(g(g(g(1))))), g(g(y0))) -> c3(F(g(0), g(g(g(g(g(1))))), g(y0)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(z0, g(g(z1)), g(g(g(g(y2))))) -> c3(F(z0, g(g(z1)), g(g(g(y2)))))
   F(g(y0), g(g(z1)), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(z1)), g(g(g(y2)))))
   F(g(g(y0)), g(g(z1)), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(z1)), g(g(g(y2)))))
   F(g(g(g(y0))), g(g(z1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(z1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(z1)), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(1)), g(g(g(g(y0))))))
   F(z0, g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(z0, g(g(g(g(y1)))), g(g(y2))))
   F(z0, g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(z0, g(g(g(y1))), g(g(g(y2)))))
   F(g(y0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(0, g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(z1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(z1)), g(g(g(g(y2))))))
   F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(z1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(y0), g(g(z1)), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(z1)), g(g(g(g(y2))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(y0), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(z0), z1, g(g(g(g(y2))))) -> c3(F(g(z0), z1, g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(0), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), z1, g(g(g(g(y2))))))
   F(g(g(g(0))), 1, g(g(g(g(y0))))) -> c3(F(g(g(g(0))), 1, g(g(g(y0)))))
   F(g(g(g(g(y0)))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), z1, g(g(g(y2)))))
   F(g(g(g(y0))), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), z1, g(g(g(g(y2))))))
   F(g(g(0)), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), 1, g(g(g(g(g(y0)))))))
   F(g(z0), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(y1), g(g(g(g(y2))))))
   F(g(z0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(0, g(1), g(g(g(g(g(y0)))))) -> c3(F(0, g(1), g(g(g(g(y0))))))
   F(z0, g(g(g(y1))), g(z2)) -> c3(F(z0, g(g(g(y1))), z2))
   F(z0, g(g(z1)), g(g(g(g(y2))))) -> c3(F(z0, g(g(z1)), g(g(g(y2)))))
   F(0, g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(1)), g(g(g(g(y0))))))
   F(z0, g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(z0, g(g(g(g(y1)))), g(g(y2))))
   F(z0, g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(z0, g(g(g(y1))), g(g(g(y2)))))
   F(0, g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(g(1))), g(g(g(g(y0))))))
   F(g(y0), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2)))
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(z0), z1, g(g(g(g(y2))))) -> c3(F(g(z0), z1, g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(0), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), z1, g(g(g(g(y2))))))
   F(g(g(g(0))), 1, g(g(g(g(y0))))) -> c3(F(g(g(g(0))), 1, g(g(g(y0)))))
   F(g(g(g(g(y0)))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), z1, g(g(g(y2)))))
   F(g(g(g(y0))), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), z1, g(g(g(g(y2))))))
   F(g(g(0)), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), 1, g(g(g(g(g(y0)))))))
   F(g(z0), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(y1), g(g(g(g(y2))))))
   F(g(z0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(0, g(1), g(g(g(g(g(y0)))))) -> c3(F(0, g(1), g(g(g(g(y0))))))
   F(z0, g(g(g(y1))), g(z2)) -> c3(F(z0, g(g(g(y1))), z2))
   F(z0, g(g(z1)), g(g(g(g(y2))))) -> c3(F(z0, g(g(z1)), g(g(g(y2)))))
   F(0, g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(1)), g(g(g(g(y0))))))
   F(z0, g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(z0, g(g(g(g(y1)))), g(g(y2))))
   F(z0, g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(z0, g(g(g(y1))), g(g(g(y2)))))
   F(0, g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(g(1))), g(g(g(g(y0))))))
   F(g(y0), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1


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

(127) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, g(y1), g(g(y2))) -> c3(F(z0, g(y1), g(y2))) by 
   F(z0, g(z1), g(g(g(y2)))) -> c3(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(z1), g(g(z2))) -> c3(F(g(g(y0)), g(z1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(z1), g(g(g(y2)))) -> c3(F(g(y0), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(z1), g(g(z2))) -> c3(F(g(g(g(y0))), g(z1), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(y0)), g(z1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(y0), g(z1), g(g(z2))) -> c3(F(g(y0), g(z1), g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(z1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(z1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(z0, g(z1), g(g(g(g(y2))))) -> c3(F(z0, g(z1), g(g(g(y2)))))
   F(g(y0), g(z1), g(g(g(g(y2))))) -> c3(F(g(y0), g(z1), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(z1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(y2)))))
   F(0, g(1), g(g(g(g(g(y0)))))) -> c3(F(0, g(1), g(g(g(g(y0))))))
   F(z0, g(g(y1)), g(g(g(g(y2))))) -> c3(F(z0, g(g(y1)), g(g(g(y2)))))
   F(g(y0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(y1)), g(g(g(y2)))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(0, g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(z0, g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(z0, g(g(g(g(y1)))), g(g(y2))))
   F(z0, g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(z0, g(g(g(y1))), g(g(g(y2)))))
   F(g(y0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(0, g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(y0), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(z1), g(g(g(g(y2))))))
   F(g(y0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(z1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(y0), g(z1), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(z1), g(g(g(g(g(y2)))))))
   F(g(y0), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(0), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(1), g(g(g(g(g(g(y0))))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(z1), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(g(y2))))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(0, g(1), g(g(g(g(g(g(y0))))))) -> c3(F(0, g(1), g(g(g(g(g(y0)))))))
   F(z0, g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(z0, g(g(y1)), g(g(g(g(y2))))))
   F(0, g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(0, g(g(1)), g(g(g(g(g(y0)))))))
   F(z0, g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(z0, g(g(g(g(y1)))), g(g(g(y2)))))
   F(z0, g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(z0, g(g(g(y1))), g(g(g(g(y2))))))
   F(0, g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(0, g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(y1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(y1)), g(g(g(g(g(g(y2))))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(g(g(y0)))))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(g(y0)))))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(g(y0)))))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(g(y0)))))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(y0))))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(z0), z1, g(g(g(g(y2))))) -> c3(F(g(z0), z1, g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(0), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), z1, g(g(g(g(y2))))))
   F(g(g(g(0))), 1, g(g(g(g(y0))))) -> c3(F(g(g(g(0))), 1, g(g(g(y0)))))
   F(g(g(g(g(y0)))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), z1, g(g(g(y2)))))
   F(g(g(g(y0))), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), z1, g(g(g(g(y2))))))
   F(g(g(0)), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), 1, g(g(g(g(g(y0)))))))
   F(g(z0), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(y1), g(g(g(g(y2))))))
   F(g(z0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(0, g(1), g(g(g(g(g(y0)))))) -> c3(F(0, g(1), g(g(g(g(y0))))))
   F(z0, g(g(g(y1))), g(z2)) -> c3(F(z0, g(g(g(y1))), z2))
   F(z0, g(g(z1)), g(g(g(g(y2))))) -> c3(F(z0, g(g(z1)), g(g(g(y2)))))
   F(0, g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(1)), g(g(g(g(y0))))))
   F(z0, g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(z0, g(g(g(g(y1)))), g(g(y2))))
   F(z0, g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(z0, g(g(g(y1))), g(g(g(y2)))))
   F(0, g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(g(1))), g(g(g(g(y0))))))
   F(g(y0), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(z0, g(z1), g(g(g(g(y2))))) -> c3(F(z0, g(z1), g(g(g(y2)))))
   F(g(y0), g(z1), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(z1), g(g(g(g(g(y2)))))))
   F(g(0), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(z1), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))))
   F(0, g(1), g(g(g(g(g(g(y0))))))) -> c3(F(0, g(1), g(g(g(g(g(y0)))))))
   F(z0, g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(z0, g(g(y1)), g(g(g(g(y2))))))
   F(0, g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(0, g(g(1)), g(g(g(g(g(y0)))))))
   F(z0, g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(z0, g(g(g(g(y1)))), g(g(g(y2)))))
   F(z0, g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(z0, g(g(g(y1))), g(g(g(g(y2))))))
   F(0, g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(0, g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(y1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(y1)), g(g(g(g(g(g(y2))))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(g(g(y0)))))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(g(y0)))))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(g(y0)))))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(g(y0)))))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(y0))))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))))
S tuples:
   F(g(g(0)), 1, z2) -> c1(F(g(0), 1, z2))
   F(g(g(g(y0))), z1, z2) -> c1(F(g(g(y0)), z1, z2))
   F(g(g(z0)), g(y1), z2) -> c1(F(g(z0), g(y1), z2))
   F(g(g(z0)), z1, g(y2)) -> c1(F(g(z0), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), z2) -> c1(F(g(z0), g(g(y1)), z2))
   F(g(g(z0)), g(y1), g(y2)) -> c1(F(g(z0), g(y1), g(y2)))
   F(g(g(0)), g(1), z2) -> c1(F(g(0), g(1), z2))
   F(g(g(g(y0))), g(y1), z2) -> c1(F(g(g(y0)), g(y1), z2))
   F(g(g(z0)), z1, g(g(y2))) -> c1(F(g(z0), z1, g(g(y2))))
   F(g(g(0)), 1, g(y0)) -> c1(F(g(0), 1, g(y0)))
   F(g(g(g(y0))), z1, g(y2)) -> c1(F(g(g(y0)), z1, g(y2)))
   F(g(g(z0)), g(g(y1)), g(y2)) -> c1(F(g(z0), g(g(y1)), g(y2)))
   F(g(g(z0)), g(y1), g(g(y2))) -> c1(F(g(z0), g(y1), g(g(y2))))
   F(g(g(0)), g(1), g(y0)) -> c1(F(g(0), g(1), g(y0)))
   F(g(g(g(y0))), g(y1), g(y2)) -> c1(F(g(g(y0)), g(y1), g(y2)))
   F(g(0), g(1), z2) -> c1(F(0, g(1), z2))
   F(g(z0), g(g(y1)), z2) -> c1(F(z0, g(g(y1)), z2))
   F(g(z0), g(z1), g(y2)) -> c1(F(z0, g(z1), g(y2)))
   F(g(z0), g(z1), g(g(y2))) -> c1(F(z0, g(z1), g(g(y2))))
   F(g(0), g(1), g(y0)) -> c1(F(0, g(1), g(y0)))
   F(g(z0), g(g(y1)), g(y2)) -> c1(F(z0, g(g(y1)), g(y2)))
   F(g(g(g(g(y0)))), g(z1), z2) -> c1(F(g(g(g(y0))), g(z1), z2))
   F(g(g(g(y0))), g(g(y1)), z2) -> c1(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(g(0))), g(1), z2) -> c1(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c1(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(z1), g(y2)) -> c1(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(y1)), g(y2)) -> c1(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(1), g(y0)) -> c1(F(g(g(0)), g(1), g(y0)))
   F(0, 1, g(y2)) -> c(F(g(g(y2)), g(g(y2)), g(y2)))
   F(0, 1, g(g(y2))) -> c(F(g(g(g(y2))), g(g(g(y2))), g(g(y2))))
   F(0, 1, g(g(g(y0)))) -> c(F(g(g(g(g(y0)))), g(g(g(g(y0)))), g(g(g(y0)))))
   F(g(0), 1, g(y0)) -> c1(F(0, 1, g(y0)))
   F(g(0), 1, g(g(y2))) -> c1(F(0, 1, g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c1(F(0, 1, g(g(g(y0)))))
   F(g(z0), z1, g(g(y2))) -> c1(F(z0, z1, g(g(y2))))
   F(g(g(g(0))), 1, g(z2)) -> c1(F(g(g(0)), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(z2)) -> c1(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(y2))) -> c1(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(z2)) -> c1(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c1(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(z2)) -> c1(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(y2))) -> c1(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(y0))) -> c1(F(g(0), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c1(F(g(0), 1, g(g(g(y0)))))
   F(0, g(1), g(y0)) -> c2(F(0, 1, g(y0)))
   F(0, g(1), g(g(y2))) -> c2(F(0, 1, g(g(y2))))
   F(0, g(1), g(g(g(y0)))) -> c2(F(0, 1, g(g(g(y0)))))
   F(z0, g(g(g(y1))), z2) -> c2(F(z0, g(g(y1)), z2))
   F(z0, g(g(z1)), g(y2)) -> c2(F(z0, g(z1), g(y2)))
   F(g(0), g(g(1)), z2) -> c2(F(g(0), g(1), z2))
   F(g(g(y0)), g(g(z1)), z2) -> c2(F(g(g(y0)), g(z1), z2))
   F(g(y0), g(g(g(y1))), z2) -> c2(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(g(z1)), g(y2)) -> c2(F(g(y0), g(z1), g(y2)))
   F(z0, g(g(z1)), g(g(y2))) -> c2(F(z0, g(z1), g(g(y2))))
   F(g(g(y0)), g(g(z1)), g(y2)) -> c2(F(g(g(y0)), g(z1), g(y2)))
   F(g(y0), g(g(z1)), g(g(y2))) -> c2(F(g(y0), g(z1), g(g(y2))))
   F(0, g(g(1)), g(y0)) -> c2(F(0, g(1), g(y0)))
   F(z0, g(g(g(y1))), g(y2)) -> c2(F(z0, g(g(y1)), g(y2)))
   F(g(0), g(g(1)), g(y0)) -> c2(F(g(0), g(1), g(y0)))
   F(g(y0), g(g(g(y1))), g(y2)) -> c2(F(g(y0), g(g(y1)), g(y2)))
   F(g(g(g(y0))), g(g(z1)), z2) -> c2(F(g(g(g(y0))), g(z1), z2))
   F(g(g(y0)), g(g(g(y1))), z2) -> c2(F(g(g(y0)), g(g(y1)), z2))
   F(g(g(0)), g(g(1)), z2) -> c2(F(g(g(0)), g(1), z2))
   F(g(g(y0)), g(g(z1)), g(g(y2))) -> c2(F(g(g(y0)), g(z1), g(g(y2))))
   F(g(g(g(y0))), g(g(z1)), g(y2)) -> c2(F(g(g(g(y0))), g(z1), g(y2)))
   F(g(g(y0)), g(g(g(y1))), g(y2)) -> c2(F(g(g(y0)), g(g(y1)), g(y2)))
   F(g(g(0)), g(g(1)), g(y0)) -> c2(F(g(g(0)), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), z2) -> c2(F(g(g(g(g(y0)))), g(z1), z2))
   F(g(g(g(y0))), g(g(g(y1))), z2) -> c2(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(g(1)), z2) -> c2(F(g(g(g(0))), g(1), z2))
   F(g(g(g(y0))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(y0))), g(z1), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(y0)))), g(z1), g(y2)))
   F(g(g(g(y0))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(y0))), g(g(y1)), g(y2)))
   F(g(g(g(0))), g(g(1)), g(y0)) -> c2(F(g(g(g(0))), g(1), g(y0)))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(z1), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(y2)))
   F(g(g(g(g(0)))), g(g(1)), g(y0)) -> c2(F(g(g(g(g(0)))), g(1), g(y0)))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(z1), g(g(y2))))
   F(0, g(g(1)), g(g(y0))) -> c2(F(0, g(1), g(g(y0))))
   F(0, g(g(1)), g(g(g(y0)))) -> c2(F(0, g(1), g(g(g(y0)))))
   F(z0, g(z1), g(g(y2))) -> c2(F(z0, z1, g(g(y2))))
   F(g(0), g(1), g(z2)) -> c2(F(g(0), 1, g(z2)))
   F(g(g(y0)), g(z1), g(z2)) -> c2(F(g(g(y0)), z1, g(z2)))
   F(g(y0), g(z1), g(g(y2))) -> c2(F(g(y0), z1, g(g(y2))))
   F(g(g(0)), g(1), g(z2)) -> c2(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), g(z1), g(z2)) -> c2(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(z1), g(g(y2))) -> c2(F(g(g(y0)), z1, g(g(y2))))
   F(g(0), g(1), g(g(y0))) -> c2(F(g(0), 1, g(g(y0))))
   F(g(0), g(1), g(g(g(y0)))) -> c2(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), g(1), g(z2)) -> c2(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), g(z1), g(z2)) -> c2(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), g(z1), g(g(y2))) -> c2(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(0)), g(1), g(g(y0))) -> c2(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c2(F(g(g(0)), 1, g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(z2)) -> c2(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(g(1))), g(z2)) -> c2(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(z2)) -> c2(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(g(y1))), g(g(y2))) -> c2(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(y2))) -> c2(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(z2)) -> c2(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c2(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(g(1))), g(g(y0))) -> c2(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c2(F(0, g(g(1)), g(g(g(y0)))))
   F(g(g(0)), g(1), z2) -> c2(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), g(z1), z2) -> c2(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(g(g(y1)))), z2) -> c2(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(g(1))), z2) -> c2(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), z2) -> c2(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(g(1))), z2) -> c2(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(0)), g(g(1)), g(g(y0))) -> c2(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c2(F(g(g(0)), g(1), g(g(g(y0)))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(z0)), g(g(g(g(y1)))), g(y2)))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(z0)), g(g(g(y1))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(0)), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(1))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(1))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(g(z0), g(g(g(g(y1)))), z2) -> c2(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(g(1))), z2) -> c2(F(g(0), g(g(1)), z2))
   F(g(0), g(g(1)), g(g(y0))) -> c2(F(g(0), g(1), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c2(F(g(0), g(1), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(z0), g(g(g(g(y1)))), g(y2)))
   F(g(0), g(g(g(g(1)))), g(y0)) -> c2(F(g(0), g(g(g(1))), g(y0)))
   F(g(z0), g(g(g(g(y1)))), g(g(y2))) -> c2(F(g(z0), g(g(g(y1))), g(g(y2))))
   F(g(g(y0)), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(y0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(g(1)))), z2) -> c2(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2) -> c2(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), z2) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), z2) -> c2(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(0)), g(g(g(1))), g(g(y0))) -> c2(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(0)), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(0))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(y2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(y2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(y2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(y2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(y0)) -> c2(F(g(g(g(g(0)))), g(g(g(g(1)))), g(y0)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(y0))) -> c2(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c2(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(z0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(z2)) -> c2(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(z0), g(g(g(g(g(y1))))), g(g(y2))) -> c2(F(g(z0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(y0))) -> c2(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c2(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)) -> c2(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)) -> c2(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))) -> c2(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
K tuples:
   F(g(0), g(1), g(z2)) -> c3(F(g(0), g(1), z2))
   F(g(g(y0)), g(y1), g(z2)) -> c3(F(g(g(y0)), g(y1), z2))
   F(g(y0), g(g(y1)), g(z2)) -> c3(F(g(y0), g(g(y1)), z2))
   F(g(y0), g(y1), g(g(y2))) -> c3(F(g(y0), g(y1), g(y2)))
   F(0, 1, g(g(y0))) -> c3(F(0, 1, g(y0)))
   F(0, 1, g(g(g(y2)))) -> c3(F(0, 1, g(g(y2))))
   F(0, 1, g(g(g(g(y0))))) -> c3(F(0, 1, g(g(g(y0)))))
   F(z0, z1, g(g(g(y2)))) -> c3(F(z0, z1, g(g(y2))))
   F(g(0), 1, g(g(z2))) -> c3(F(g(0), 1, g(z2)))
   F(g(g(y0)), z1, g(g(z2))) -> c3(F(g(g(y0)), z1, g(z2)))
   F(g(y0), z1, g(g(g(y2)))) -> c3(F(g(y0), z1, g(g(y2))))
   F(0, g(1), g(g(z2))) -> c3(F(0, g(1), g(z2)))
   F(z0, g(g(y1)), g(g(z2))) -> c3(F(z0, g(g(y1)), g(z2)))
   F(z0, g(y1), g(g(g(y2)))) -> c3(F(z0, g(y1), g(g(y2))))
   F(g(0), g(1), g(g(z2))) -> c3(F(g(0), g(1), g(z2)))
   F(g(g(y0)), g(y1), g(g(z2))) -> c3(F(g(g(y0)), g(y1), g(z2)))
   F(g(y0), g(g(y1)), g(g(z2))) -> c3(F(g(y0), g(g(y1)), g(z2)))
   F(g(y0), g(y1), g(g(g(y2)))) -> c3(F(g(y0), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(z2))) -> c3(F(g(g(0)), 1, g(z2)))
   F(g(g(g(y0))), z1, g(g(z2))) -> c3(F(g(g(g(y0))), z1, g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(z2))) -> c3(F(g(g(y0)), g(g(y1)), g(z2)))
   F(g(g(0)), g(1), g(g(z2))) -> c3(F(g(g(0)), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(z2))) -> c3(F(g(g(g(y0))), g(y1), g(z2)))
   F(g(g(y0)), z1, g(g(g(y2)))) -> c3(F(g(g(y0)), z1, g(g(y2))))
   F(g(g(y0)), g(y1), g(g(g(y2)))) -> c3(F(g(g(y0)), g(y1), g(g(y2))))
   F(g(g(g(g(y0)))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(y1), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(y1)), g(z2)))
   F(g(g(g(0))), g(1), g(g(z2))) -> c3(F(g(g(g(0))), g(1), g(z2)))
   F(g(g(g(y0))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(y1), g(g(y2))))
   F(g(0), 1, g(g(g(y0)))) -> c3(F(g(0), 1, g(g(y0))))
   F(g(0), 1, g(g(g(g(y0))))) -> c3(F(g(0), 1, g(g(g(y0)))))
   F(g(g(g(0))), 1, g(g(z2))) -> c3(F(g(g(g(0))), 1, g(z2)))
   F(g(g(g(g(y0)))), z1, g(g(z2))) -> c3(F(g(g(g(g(y0)))), z1, g(z2)))
   F(g(g(g(y0))), z1, g(g(g(y2)))) -> c3(F(g(g(g(y0))), z1, g(g(y2))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(z2)))
   F(g(g(g(g(0)))), g(1), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(1), g(z2)))
   F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(y2))))
   F(g(g(0)), 1, g(g(g(y0)))) -> c3(F(g(g(0)), 1, g(g(y0))))
   F(g(g(0)), 1, g(g(g(g(y0))))) -> c3(F(g(g(0)), 1, g(g(g(y0)))))
   F(0, g(1), g(g(g(y0)))) -> c3(F(0, g(1), g(g(y0))))
   F(0, g(1), g(g(g(g(y0))))) -> c3(F(0, g(1), g(g(g(y0)))))
   F(z0, g(g(g(y1))), g(g(z2))) -> c3(F(z0, g(g(g(y1))), g(z2)))
   F(g(0), g(g(1)), g(g(z2))) -> c3(F(g(0), g(g(1)), g(z2)))
   F(g(y0), g(g(g(y1))), g(g(z2))) -> c3(F(g(y0), g(g(g(y1))), g(z2)))
   F(z0, g(g(y1)), g(g(g(y2)))) -> c3(F(z0, g(g(y1)), g(g(y2))))
   F(g(y0), g(g(y1)), g(g(g(y2)))) -> c3(F(g(y0), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(z2))) -> c3(F(0, g(g(1)), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(y1))), g(z2)))
   F(g(g(0)), g(g(1)), g(g(z2))) -> c3(F(g(g(0)), g(g(1)), g(z2)))
   F(g(g(y0)), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(y1)), g(g(y2))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(z2)))
   F(g(g(g(0))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(0))), g(g(1)), g(z2)))
   F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(0)))), g(g(1)), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(z2)))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(y2))))
   F(0, g(g(1)), g(g(g(y0)))) -> c3(F(0, g(g(1)), g(g(y0))))
   F(0, g(g(1)), g(g(g(g(y0))))) -> c3(F(0, g(g(1)), g(g(g(y0)))))
   F(g(0), g(1), g(g(g(y0)))) -> c3(F(g(0), g(1), g(g(y0))))
   F(g(0), g(1), g(g(g(g(y0))))) -> c3(F(g(0), g(1), g(g(g(y0)))))
   F(g(g(0)), g(1), g(g(g(y0)))) -> c3(F(g(g(0)), g(1), g(g(y0))))
   F(g(g(0)), g(1), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(1), g(g(g(y0)))))
   F(z0, g(g(g(g(y1)))), g(g(z2))) -> c3(F(z0, g(g(g(g(y1)))), g(z2)))
   F(g(0), g(g(g(1))), g(g(z2))) -> c3(F(g(0), g(g(g(1))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(y1)))), g(z2)))
   F(z0, g(g(g(y1))), g(g(g(y2)))) -> c3(F(z0, g(g(g(y1))), g(g(y2))))
   F(g(y0), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(z2))) -> c3(F(0, g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(z2)))
   F(g(g(0)), g(g(g(1))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(1))), g(z2)))
   F(g(g(y0)), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(y2))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(0))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(1))), g(z2)))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(y2))))
   F(0, g(g(g(1))), g(g(g(y0)))) -> c3(F(0, g(g(g(1))), g(g(y0))))
   F(0, g(g(g(1))), g(g(g(g(y0))))) -> c3(F(0, g(g(g(1))), g(g(g(y0)))))
   F(g(g(0)), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(1)), g(g(y0))))
   F(g(g(0)), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(y2))))
   F(g(0), g(g(1)), g(g(g(y0)))) -> c3(F(g(0), g(g(1)), g(g(y0))))
   F(g(0), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(0), g(g(1)), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(z2)))
   F(g(0), g(g(g(g(1)))), g(g(z2))) -> c3(F(g(0), g(g(g(g(1)))), g(z2)))
   F(g(y0), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(0)), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(1))), g(g(y0))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(0), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(1))), g(g(y0))))
   F(g(0), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(1))), g(g(g(y0)))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(0), g(g(g(g(g(1))))), g(g(z2))) -> c3(F(g(0), g(g(g(g(g(1))))), g(z2)))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(y0))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(z2))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(z2))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(z2)))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(z2))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(z2)))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(0, 1, g(g(g(g(g(y0)))))) -> c3(F(0, 1, g(g(g(g(y0))))))
   F(g(0), 1, g(g(g(g(g(y0)))))) -> c3(F(g(0), 1, g(g(g(g(y0))))))
   F(g(g(0)), 1, g(z2)) -> c3(F(g(g(0)), 1, z2))
   F(g(g(g(y0))), z1, g(z2)) -> c3(F(g(g(g(y0))), z1, z2))
   F(g(g(z0)), g(g(y1)), g(z2)) -> c3(F(g(g(z0)), g(g(y1)), z2))
   F(g(g(0)), g(1), g(z2)) -> c3(F(g(g(0)), g(1), z2))
   F(g(g(g(y0))), g(y1), g(z2)) -> c3(F(g(g(g(y0))), g(y1), z2))
   F(g(g(g(g(y0)))), g(y1), g(z2)) -> c3(F(g(g(g(g(y0)))), g(y1), z2))
   F(g(g(g(y0))), g(g(y1)), g(z2)) -> c3(F(g(g(g(y0))), g(g(y1)), z2))
   F(g(g(g(0))), g(1), g(z2)) -> c3(F(g(g(g(0))), g(1), z2))
   F(g(g(z0)), g(g(g(y1))), g(z2)) -> c3(F(g(g(z0)), g(g(g(y1))), z2))
   F(g(g(0)), g(g(1)), g(z2)) -> c3(F(g(g(0)), g(g(1)), z2))
   F(g(g(g(g(y0)))), g(g(y1)), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(y1)), z2))
   F(g(g(g(y0))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(y1))), z2))
   F(g(g(g(0))), g(g(1)), g(z2)) -> c3(F(g(g(g(0))), g(g(1)), z2))
   F(g(g(z0)), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(y1)))), z2))
   F(g(g(0)), g(g(g(1))), g(z2)) -> c3(F(g(g(0)), g(g(g(1))), z2))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), z2))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), z2))
   F(g(g(g(0))), g(g(g(1))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(1))), z2))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), z2))
   F(g(g(0)), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(0)), g(g(g(g(1)))), z2))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(z2)) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), z2))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(z2)) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), z2))
   F(g(g(g(0))), g(g(g(g(1)))), g(z2)) -> c3(F(g(g(g(0))), g(g(g(g(1)))), z2))
   F(g(g(z0)), z1, g(g(g(g(y2))))) -> c3(F(g(g(z0)), z1, g(g(g(y2)))))
   F(g(g(z0)), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(1), g(g(y0))))
   F(g(g(g(y0))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(y2)))))
   F(g(g(g(0))), 1, g(g(g(y0)))) -> c3(F(g(g(g(0))), 1, g(g(y0))))
   F(g(g(g(g(y0)))), z1, g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), z1, g(g(y2))))
   F(g(g(g(y0))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), z1, g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(y2))))
   F(g(g(g(g(0)))), g(1), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(1), g(g(y0))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(y2)))))
   F(g(g(0)), 1, g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), 1, g(g(g(g(y0))))))
   F(g(g(z0)), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(0))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(1)), g(g(y0))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(y2))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(y2)))))
   F(g(g(0)), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(1), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(z0)), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(z0)), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(y2))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(y0))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(z0), g(g(g(y1))), g(z2)) -> c3(F(g(z0), g(g(g(y1))), z2))
   F(g(0), g(g(1)), g(z2)) -> c3(F(g(0), g(g(1)), z2))
   F(g(z0), g(g(g(g(y1)))), g(z2)) -> c3(F(g(z0), g(g(g(g(y1)))), z2))
   F(g(0), g(g(g(1))), g(z2)) -> c3(F(g(0), g(g(g(1))), z2))
   F(g(z0), g(z1), g(g(g(g(y2))))) -> c3(F(g(z0), g(z1), g(g(g(y2)))))
   F(g(z0), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(y1)), g(g(g(y2)))))
   F(g(0), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(1), g(g(g(g(y0))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(y2)))))
   F(g(0), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(1)), g(g(g(g(y0))))))
   F(g(0), g(g(g(g(1)))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(1)))), g(g(y0))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(y0))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(y2))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(y0))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(y0)), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(y2))))))
   F(g(g(g(0))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(1), g(g(g(y0)))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(y2)))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(y0)))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(z0), z1, g(g(g(g(y2))))) -> c3(F(g(z0), z1, g(g(g(y2)))))
   F(g(0), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(0), 1, g(g(g(g(g(y0)))))))
   F(g(g(y0)), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), z1, g(g(g(g(y2))))))
   F(g(g(g(0))), 1, g(g(g(g(y0))))) -> c3(F(g(g(g(0))), 1, g(g(g(y0)))))
   F(g(g(g(g(y0)))), z1, g(g(g(g(y2))))) -> c3(F(g(g(g(g(y0)))), z1, g(g(g(y2)))))
   F(g(g(g(y0))), z1, g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), z1, g(g(g(g(y2))))))
   F(g(g(0)), 1, g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), 1, g(g(g(g(g(y0)))))))
   F(g(z0), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(y1), g(g(g(g(y2))))))
   F(g(z0), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(y1)), g(g(g(g(y2))))))
   F(g(0), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(1), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))) -> c3(F(g(z0), g(g(g(g(g(g(y1)))))), g(g(g(y2)))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(y0)))))
   F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(z0), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(y1), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(y1), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(y2))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(y0))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(0, g(1), g(g(g(g(g(y0)))))) -> c3(F(0, g(1), g(g(g(g(y0))))))
   F(z0, g(g(g(y1))), g(z2)) -> c3(F(z0, g(g(g(y1))), z2))
   F(z0, g(g(z1)), g(g(g(g(y2))))) -> c3(F(z0, g(g(z1)), g(g(g(y2)))))
   F(0, g(g(1)), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(1)), g(g(g(g(y0))))))
   F(z0, g(g(g(g(y1)))), g(g(g(y2)))) -> c3(F(z0, g(g(g(g(y1)))), g(g(y2))))
   F(z0, g(g(g(y1))), g(g(g(g(y2))))) -> c3(F(z0, g(g(g(y1))), g(g(g(y2)))))
   F(0, g(g(g(1))), g(g(g(g(g(y0)))))) -> c3(F(0, g(g(g(1))), g(g(g(g(y0))))))
   F(g(y0), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(y2))))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(g(y0))))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(z1)), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(z1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(y0)))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(z0, g(z1), g(g(g(g(y2))))) -> c3(F(z0, g(z1), g(g(g(y2)))))
   F(g(y0), g(z1), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(z1), g(g(g(g(g(y2)))))))
   F(g(0), g(1), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(0), g(1), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(z1), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(z1), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(0))), g(1), g(g(g(g(g(y0)))))))
   F(g(g(g(y0))), g(z1), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(z1), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(g(g(y2))))))) -> c3(F(g(g(g(g(g(y0))))), g(z1), g(g(g(g(g(y2)))))))
   F(g(g(g(g(0)))), g(1), g(g(g(g(g(g(y0))))))) -> c3(F(g(g(g(g(0)))), g(1), g(g(g(g(g(y0)))))))
   F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(z1), g(g(g(g(g(g(y2))))))))
   F(g(g(0)), g(1), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(g(0)), g(1), g(g(g(g(g(g(g(y0)))))))))
   F(0, g(1), g(g(g(g(g(g(y0))))))) -> c3(F(0, g(1), g(g(g(g(g(y0)))))))
   F(z0, g(g(y1)), g(g(g(g(g(y2)))))) -> c3(F(z0, g(g(y1)), g(g(g(g(y2))))))
   F(0, g(g(1)), g(g(g(g(g(g(y0))))))) -> c3(F(0, g(g(1)), g(g(g(g(g(y0)))))))
   F(z0, g(g(g(g(y1)))), g(g(g(g(y2))))) -> c3(F(z0, g(g(g(g(y1)))), g(g(g(y2)))))
   F(z0, g(g(g(y1))), g(g(g(g(g(y2)))))) -> c3(F(z0, g(g(g(y1))), g(g(g(g(y2))))))
   F(0, g(g(g(1))), g(g(g(g(g(g(y0))))))) -> c3(F(0, g(g(g(1))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(y1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(y1)), g(g(g(g(g(g(y2))))))))
   F(g(y0), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(0), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(0), g(g(1)), g(g(g(g(g(g(g(y0)))))))))
   F(g(0), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(g(1)))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(0), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))) -> c3(F(g(0), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))))
   F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))) -> c3(F(g(y0), g(g(g(g(g(g(y1)))))), g(g(g(g(g(y2)))))))
   F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))) -> c3(F(g(0), g(g(g(g(g(1))))), g(g(g(g(g(y0)))))))
   F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(y0), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(y1)), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(y1)), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(y1)), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(1)), g(g(g(g(g(g(y0))))))))
   F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(y1))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(1))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(y1))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(g(y0)))))))))) -> c3(F(g(g(0)), g(g(1)), g(g(g(g(g(g(g(g(y0))))))))))
   F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(y1)))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(1)))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(y1)))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(g(y0)))))))))) -> c3(F(g(g(0)), g(g(g(1))), g(g(g(g(g(g(g(g(y0))))))))))
   F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(y1))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(1))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(y1))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(g(y0)))))))))) -> c3(F(g(g(0)), g(g(g(g(1)))), g(g(g(g(g(g(g(g(y0))))))))))
   F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))))
   F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(y0)), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(0)), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(0))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(y0))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))))
   F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(g(y0))))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(g(y2)))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(g(y1))))))), g(g(g(g(g(g(y2))))))))
   F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(g(y0)))))))) -> c3(F(g(g(g(g(0)))), g(g(g(g(g(g(1)))))), g(g(g(g(g(g(y0))))))))
   F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(g(y2))))))))) -> c3(F(g(g(g(g(y0)))), g(g(g(g(g(g(y1)))))), g(g(g(g(g(g(g(y2)))))))))
Defined Rule Symbols:none

Defined Pair Symbols:   F_3

Compound Symbols:   c3_1, c1_1, c_1, c2_1